On Orlicz sequence spaces

DOI10.1007/BF02771656zbMath0227.46042MaRDI QIDQ2549473

Publication date: 1971

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sequence spaces (including Köthe sequence spaces) (46A45) Banach sequence spaces (46B45)

Related Items

Operator ideal of Norlund-type sequence spaces ⋮ The entire sequence over Musielak $p$-metric space ⋮ Seminormed double sequence spaces of four-dimensional matrix and Musielak-Orlicz function ⋮ Lack of isomorphic embeddings of symmetric function spaces into operator ideals ⋮ The uniform nonequivalence of $L_ p$ and $\ell_ p$ ⋮ Strongly $(V_{\sigma},\lambda,q)$-summable sequences defined by Orlicz functions ⋮ Orlicz lacunary sequence spaces of $l$-fractional difference operators ⋮ On power bounded operators ⋮ Applications of statistical convergence to $n$-normed spaces ⋮ Invertibility of ``large submatrices with applications to the geometry of Banach spaces and harmonic analysis ⋮ Mappings of type special space of sequences ⋮ The spectrum operator of $\chi^{2}$ sequence space defined by Musielak Orlicz function ⋮ The metrical interpretation of superreflexivity in Banach spaces ⋮ The double almost $(\lambda_{m}\mu_{n})$ convergence in $\Gamma^{2}$-Riesz space defined by a Musielak-Orlicz function ⋮ The $\int \chi^{2\lambda I}$ statistical convergence of fuzzy numbers over $p$-metric space. II ⋮ Orlicz difference sequence spaces generated by infinite matrices and de la Vallée-Poussin mean of order $\alpha$ ⋮ Generalized difference strongly summable sequence spaces of fuzzy real numbers defined by ideal convergence and Orlicz function ⋮ On vector valued sequence spaces $h_{N}(E_{k}), \ell _{M}(B(E_{k},Y))$ and $\ell_{M}(E^{\prime}_{k})$ ⋮ On Arazy's problem concerning isomorphic embeddings of ideals of compact operators ⋮ On $\ell ^ p$-complemented copies in Orlicz spaces ⋮ Generalized difference sequences of fuzzy numbers ⋮ Double almost lacunary statistical convergence of order $\alpha$ ⋮ Mappings of type Orlicz and generalized Cesáro sequence space ⋮ Existence of homoclinic solutions for $p(n)$-Laplacian Hamiltonian systems on Orlicz sequence spaces ⋮ On Orlicz-power series spaces ⋮ The generalized $\chi^{2}$ sequence spaces over $p$-metric spaces defined by Musielak ⋮ On some ideal convergent multiplier sequence spaces using de la Vallee Poussin mean and Zweier operator ⋮ Some $I$-convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz functions ⋮ $\mu$-statistical convergent double lacunary sequence spaces ⋮ Double almost statistical convergence of order $\alpha$ ⋮ $\mu$-lacunary $\chi_{A_{uv}}^2$-convergence of order $\alpha$ with $p$-metric defined by $mn$ sequence of moduli Musielak ⋮ Some double sequence spaces defined by a sequence of Orlicz functions over $n$-normed spaces ⋮ Some $I$-convergent sequence spaces defined by Orlicz functions ⋮ The sequence space $E_{n}^{q}\left( M,p,s\right) $ and $N_{k}$-lacunary statistical convergence ⋮ Some new sequence spaces of fuzzy numbers defined by Orlicz functions using a fuzzy metric ⋮ On paranormed ideal convergent generalized difference strongly summable sequence spaces defined over $n$-normed spaces ⋮ Contractive projections on Banach algebras ⋮ Double sequence spaces by means of Orlicz functions ⋮ Characterization of entire sequences via double Orlicz space ⋮ On paranormed Zweier ideal convergent sequence spaces defined by Orlicz function ⋮ Ideal convergent sequence spaces over $p$-metric spaces defined by Musielak-modulus functions ⋮ Multiplication operators on Orlicz generalized difference (sss) ⋮ Double sequence spaces defined over an $n$-normed sequence space ⋮ Lacunary summable sequence spaces of fuzzy numbers defined by ideal convergence and an Orlicz function ⋮ Multiple Rademacher series in symmetric spaces ⋮ Bertrand curves of $\mathrm{AW}(k)$-type in the equiform geometry of the Galilean space ⋮ New classes of generalized seminormed difference sequence spaces ⋮ On some classes of double difference sequences of interval numbers ⋮ Some new classes of generalized difference strongly summable $n$-normed sequence spaces defined by ideal convergence and Orlicz function ⋮ New difference sequence spaces defined by Musielak-Orlicz function ⋮ On ground states of discrete $p(k)$-Laplacian systems in generalized Orlicz sequence spaces ⋮ Some new lacunary strong convergent vector-valued sequence spaces ⋮ A class of sequences defined by weak ideal convergence and Musielak-Orlicz function ⋮ Some properties of the sequence space $E^q_n(\mathcal M,p,s, \|\cdot, \dots, \cdot\|)$ ⋮ Orlicz generalized difference sequence space and the linked pre-quasi operator ideal ⋮ Uniqueness of symmetric basis in quasi-Banach spaces ⋮ Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces ⋮ 1-greedy renormings of Garling sequence spaces ⋮ Some seminormed difference sequence spaces over $n$-normed spaces defined by a Musielak-Orlicz function of order $(\alpha, \beta)$ ⋮ An arbitrarily distortable Banach space ⋮ Some Orlicz extended $\mathcal{I}$-convergent $A$-summable classes of sequences of fuzzy numbers ⋮ Some multiplier generalized difference sequence spaces over $n$-normed spaces defined by a Musielak-Orlicz function ⋮ Strongly $(V^\lambda , A, \Delta ^n_{[vm)}, p)$-summable sequence spaces defined by an Orlicz function ⋮ A new class of sequences related to the $l_{p}$ spaces defined by sequences of Orlicz functions ⋮ Double sequence spaces over $n$-normed spaces defined by a sequence of Orlicz functions ⋮ Double sequences and Orlicz functions ⋮ On certain generalized paranormed spaces ⋮ The sequence space $| \overline N_p|(M, r, q, s)$ on seminormed spaces ⋮ On a class of generalized lacunary difference sequence spaces defined by Orlicz functions ⋮ On the Orlicz function spaces $L_M(0,\infty)$ ⋮ On paranorm $\mathrm{BV}_\sigma$ $I$-convergent double sequence spaces defined by an Orlicz function ⋮ Sequence spaces defined by Musielak-Orlicz function over $n$-normed spaces ⋮ An extension of modular sequence spaces ⋮ On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions ⋮ Generalized difference $\lambda $-sequence spaces defined by ideal convergence and the Musielak-Orlicz function ⋮ Sous-espaces de $L^1$ ⋮ The uniform approximation property in Orlicz spaces ⋮ Equidistributed random variables in $L_{p,q}$ ⋮ Two applications of Boolean valued analysis ⋮ Derive convexe d'une loi de probabilité et lois stables. Application à un problème d'isomorphisme ⋮ Banach spaces with a unique greedy basis ⋮ The geometry of normed spaces ⋮ Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems ⋮ The spectrum generated by $s$-numbers and pre-quasi normed Orlicz-Cesàro mean sequence spaces ⋮ On some spaces of Cesàro sequences of fuzzy numbers associated with $\lambda $-convergence and Orlicz function ⋮ Matrix transformations of Nörlund-Orlicz difference sequence spaces of nonabsolute type and their Toeplitz duals ⋮ Generalized vector valued paranormed sequence space using Orlicz function ⋮ Small operator ideals formed by $s$ numbers on generalized Cesàro and Orlicz sequence spaces ⋮ Small pre-quasi Banach operator ideals of type Orlicz-Cesáro mean sequence spaces ⋮ Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function ⋮ Applications of non-Newtonian calculus for classical spaces and Orlicz functions ⋮ Some properties of pre-quasi norm on Orlicz sequence space ⋮ On perfectly homogeneous bases in quasi-Banach spaces ⋮ On generalized paranormed statistically convergent sequence spaces defined by Orlicz function ⋮ $\lambda $-difference sequence spaces of fuzzy numbers ⋮ A last theorem of Kalton and finiteness of Connes' integral ⋮ On symmetric basic sequences in Lorentz sequence spaces. II ⋮ Generalized vector-valued paranormed sequence spaces determined by a sequence of Orlicz functions ⋮ Generalized spaces of double sequences for Orlicz functions and bounded-regular matrices over $n$-normed spaces ⋮ Algebraic duals of some sets of difference sequences defined by Orlicz functions ⋮ On isomorphisms of algebras of entire symmetric functions on Banach spaces ⋮ Linear isomorphic spaces of Cesàro-Nörlund operator, their duals and matrix transformations ⋮ On Orlicz sequence algebras ⋮ On weighted statistical convergence of difference sequences of fractional order ⋮ Norm inequalities involving upper bounds for certain matrix operators on Orlicz-Euler and Orlicz-Taylor double sequence spaces ⋮ Representation theorems for regular operators ⋮ Relative uniform convergence of double sequence of positive linear functions defined by Orlicz function ⋮ Unnamed Item ⋮ The geometry of Minkowski spaces -- a survey. I ⋮ Defining some new $n$-tuple sequence spaces related to $l_p$ space with the help of Orlicz function ⋮ ON ASYMPTOTICALLY f-ROUGH STATISTICAL EQUIVALENT OF TRIPLE SEQUENCES ⋮ Unnamed Item ⋮ The Cesàro $\chi ^{2}$ of tensor products in Orlicz sequence spaces ⋮ Generalized difference sequence space defined by |$$ \bar N $$, p k| summability and an Orlicz function in seminormed space ⋮ Some sequence spaces defined by a Musielak-Orlicz function in n-normed spaces ⋮ Unnamed Item ⋮ On a class of difference sequences related to the ℓp space defined by Orlicz functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ An Orlicz extension of difference sequences on real linear $n$-normed spaces ⋮ On some I -convergent generalized difference sequence spaces associated with multiplier sequence defined by a sequence of modulli ⋮ Sequence spaces defined via Euler method and matrix transformations ⋮ Unnamed Item ⋮ Almost strongly Orlicz double sequence spaces of regular matrices and their applications to statistical convergence ⋮ On some difference sequence spaces defined by a sequence of Orlicz functions ⋮ Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers ⋮ $I$-convergent sequences of fuzzy real numbers defined by Orlicz function ⋮ On a new space $m^2(M, A, \phi, p)$ of double sequences ⋮ Isolated points of spaces of homomorphisms from ordered AL-algebras ⋮ Some new sequence spaces defined by bounded variation in 2-normed spaces ⋮ Complete paranormed Orlicz Lorentz sequence spaces over $n$-normed spaces ⋮ Generalized Difference Sequence Spaces of Fractional Order Defined by Orlicz Functions ⋮ Some sequence spaces over $n$-normed spaces defined by fractional difference operator and Musielak-Orlicz function ⋮ Fractional difference double sequences of fuzzy numbers ⋮ Hardy-Lorentz spaces for $\mathbf{B}$-valued martingales ⋮ Some classes of sequence spaces defined by a Musielak-Orlicz function ⋮ Unnamed Item ⋮ Geometric difference of six-dimensional Riesz almost lacunary rough statistical convergence in probabilistic space of $\chi_{f}^{3}$ ⋮ New classes of sequence spaces defined by Orlicz function ⋮ The intuitionistic triple $\chi$ of ideal fuzzy real numbers over $p$-metric spaces defined by Musielak Orlicz function ⋮ Unnamed Item ⋮ Developments in Schauder basis theory ⋮ On two-valued measure and double statistical convergence in 2-normed spaces ⋮ Some properties of the sequence space ⋮ On a Class of Sequences Related to $p$-Absolutely Summable Sequences in Metric Space Defined by Orlicz Functions ⋮ On generalized statistical convergence of order $\alpha$ of difference sequences ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Orlicz-Quasi-Cauchy double sequence spaces for RH-regular matrix ⋮ New Classes of Statistically Pre-Cauchy Triple Sequences of Fuzzy Numbers Defined by Orlicz Function ⋮ Some new triple sequence spaces over n-normed space ⋮ A relation of Banach limit and difference matrix to generate some Orlicz sequence spaces ⋮ COMPUTATION OF THE KÖTHE-TOEPLITZ DUAL OF SOME SETS OF SEQUENCES OF FUZZY NUMBERS ⋮ Re exivity of vector-valued Köthe-Orlicz sequence spaces ⋮ ON ASYMPTOTIC UNIFORM SMOOTHNESS AND NONLINEAR GEOMETRY OF BANACH SPACES ⋮ ON PARANORMED TYPE p-ABSOLUTELY SUMMABLE UNCERTAIN SEQUENCE SPACES DEFINED BY ORLICZ FUNCTIONS ⋮ The Generalized difference of $d left(chi^{3textit{I}}right)$ of fuzzy real numbers over $p$ metric spaces defined by Musielak Orlicz function ⋮ Unnamed Item ⋮ On some new generalized difference sequence spaces on seminormed spaces defined by a sequence of Orlicz functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Orlicz sequence spaces without local convexity ⋮ Unnamed Item ⋮ Unnamed Item ⋮ -Lacunary -convergence of order with p-metric defined by mnk sequence of moduli Musielak—Orlicz function ⋮ Approximative Properties of Diagonal Operators in Orlicz Spaces ⋮ Some classes of ideal convergent sequences and generalized difference matrix operator ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On generalized geometric difference of six dimensional rough ideal convergent of triple sequence defined by Musielak-Orlicz function ⋮ A dichotomy for subsymmetric basic sequences with applications to Garling spaces ⋮ Unnamed Item ⋮ On Some I-Convergent Double Sequence Spaces of Fuzzy Real Numbers Defined by Modulus Function ⋮ Triple sets of -summable sequences of fuzzy numbers defined by an Orlicz function ⋮ Some generalized double lacunary Zweier convergent sequence spaces ⋮ Statistical convergence of complex uncertain sequences defined by Orlicz function ⋮ Unnamed Item ⋮ Dual complements for domains of ℂ^n ⋮ Some Applications of Summability Theory ⋮ Vector valued double sequence spaces defined by Orlicz function ⋮ THE GENERALIZED NON-ABSOLUTE TYPE OF TRIPLE Γ3 SEQUENCE SPACES DEFINED MUSIELAK-ORLICZ FUNCTION ⋮ On Orlicz sequence spaces. II ⋮ Strongly almost lacunary $I$-convergent sequences ⋮ Some generalized difference sequence spaces defined by ideal convergence and Musielak-Orlicz function ⋮ A remark on symmetric bases ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On Orlicz sequence spaces. III ⋮ Sur un théorème de J. L. Krivine concernant la caractérisation des classes d'espaces isomorphes à des espaces d'Orlicz généralises et des classes voisines ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On an isomorphic Banach-Mazur rotation problem and maximal norms in Banach spaces ⋮ Unnamed Item ⋮ Topological properties of some sequences defined over n−normed spaces ⋮ Singular traces and perturbation formulae of higher order ⋮ Unnamed Item

Cites Work