Similarities and differences between real and complex Banach spaces: an overview and recent developments
From MaRDI portal
Publication:2121668
DOI10.1007/s13398-022-01222-8zbMath1497.46028arXiv2107.03740OpenAlexW3179620458MaRDI QIDQ2121668
Antonio M. Peralta, Mohammad Sal Moslehian, Gustavo A. Muñoz-Fernández, Juan B. Seoane-Sepúlveda
Publication date: 4 April 2022
Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.03740
Normed linear spaces and Banach spaces; Banach lattices (46B99) Determinants, permanents, traces, other special matrix functions (15A15) (Spaces of) multilinear mappings, polynomials (46G25) Inequalities and extremum problems in real or complex geometry (51M16) Operators on Banach spaces (47B01)
Related Items
Relay fusion frames in Banach spaces ⋮ Refinements of the generalized numerical radius of Heinz-type inequalities ⋮ Approximate isosceles \(\omega\)-orthogonality and approximate \(\omega\)-parallelism ⋮ Fractional boundary value problem in complex domain ⋮ An orthogonality relation in complex normed spaces based on norm derivatives ⋮ Conditional expectations in complete normed complex algebras satisfying the von Neumann inequality
Cites Work
- Banach spaces of continuous functions as dual spaces
- Complex structures on Banach spaces with a subsymmetric basis
- The Bohr radius of the \(n\)-dimensional polydisk is equivalent to \(\sqrt{(\log n) / n}\)
- The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal
- A Kowalski-Słodkowski theorem for 2-local \({}^\ast\)-homomorphisms on von Neumann algebras
- A treatment of the Cauchy-Schwarz inequality in \(C^{*}\)-modules
- Geometric characterization of tripotents in real and complex JB\(^{*}\)-triples
- The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive
- New upper bounds for the constants in the Bohnenblust-Hille inequality
- Unitary operators in real von Neumann algebras
- Bounded and unbounded polynomials and multilinear forms: Characterizing continuity
- A superreflexive Banach space X with L(X) admitting a homomorphism onto the Banach algebra C(\(\beta\) N)
- Solution of the contractive projection problem
- Geometrical properties of the unit sphere of Banach algebras
- A generalization of an inequality of V. Markov to multivariate polynomials. II
- Some open problems and conjectures associated with the invariant subspace problem
- Zeroes of polynomials on \(\ell _{\infty }\)
- Odd degree polynomials on real Banach spaces
- Radius of analyticity of a power series on real Banach spaces
- Squared chaotic random variables: new moment inequalities with applications
- The plank problem for symmetric bodies
- The Bishop-Phelps-Bollobás theorem for operators
- Pfaffians, Hafnians and products of real linear functionals
- A proof of Markov's theorem for polynomials on Banach spaces
- Banach space characterizations of unitaries: a survey
- Geometric unitaries in JB-algebras
- A characterization of ternary rings of operators
- A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces
- Real normed Jordan Banach algebras with an involution
- Conditional expectation and bicontractive projections on Jordan \(C^ *\)- algebras and their generalizations
- Weighted polynomial inequalities
- On the invariant subspace problem for Banach spaces
- Gaussian variables, polynomials and permanents
- A generalization of an inequality of V Markov to multivariate polynomials
- Affine geometric proofs of the Banach Stone theorems of Kadison and Kaup
- A primer on spectral theory
- The separable extension problem
- Jordan \(C^*\)-algebras
- A holomorphic characterization of Jordan \(C^*\)-algebras
- On multivariate polynomials of least deviation from zero on the unit cube
- Geometry of spaces of polynomials
- On automatic continuity and three problems of ``The Scottish Book concerning the boundedness of polynomial functionals
- Averages of norms and quasi-norms
- Extremal homogeneous polynomials on real normed spaces
- Contractive projections and isometries in sequence spaces
- Characterization of real inner product spaces by means of symmetric bilinear forms
- On real Cartan factors
- A Bernstein-Markov theorem for normed spaces
- The norm of a complex Banach lattice
- A characterization of real Hilbert spaces using the Bochnak complexification norm
- On real operator spaces
- Zeros of polynomials on Banach spaces: The real story
- Complexifications of real operator spaces
- On the absolute convergence of Dirichlet series
- Separate weak\(^*\)-continuity of the triple product in dual real JB\(^*\)-triples
- Non-linear plank problems and polynomial inequalities
- A Gleason-Kahane-Żelazko theorem for the Dirichlet space
- Weak-2-local isometries on uniform algebras and Lipschitz algebras
- Radius of analyticity of analytic functions on Banach spaces
- Physical applications of homogeneous balls. With the assistance of Tzvi Scarr
- Linear polarization constants of Hilbert spaces
- Some character generating functions on Banach algebras
- Reflexivity of the isometry group of some classical spaces.
- A note on complex \(P_1\) spaces
- Theory of operator algebras. III
- Subdifferentiability of the norm and the Banach--Stone theorem for real and complex JB*-triples
- On real forms of JB\(^*\)-triples
- A counterexample to the Bishop-Phelps theorem in complex spaces
- Every non-smooth 2-dimensional Banach space has the Mazur-Ulam property
- Complexifications of real Banach spaces and their isometries
- Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces
- Quantitative and qualitative estimates on the norm of products of polynomials
- 2-iso-reflexivity of pointed Lipschitz spaces
- Extension of isometries from the unit sphere of a rank-2 Cartan factor
- A new approach towards estimating the \(n\)-dimensional Bohr radius
- Every $2$-dimensional Banach space has the Mazur-Ulam property
- A Banach space with a countable infinite number of complex structures
- The Bishop-Phelps-Bollobás theorem for operators on \(L_1(\mu)\)
- Algebraic reflexivity of the isometry group of some spaces of Lipschitz functions
- On 2-local *-automorphisms and 2-local isometries of \(\mathscr{B}(H)\)
- Uniqueness of complex structure and real hereditarily indecomposable Banach spaces
- Zeroes of real polynomials on \(C(K)\) spaces
- Matrix KSGNS construction and a Radon-Nikodym type theorem
- On the zero-set of real polynomials in non-separable Banach spaces
- A geometric estimate on the norm of product of functionals
- Zero sets of polynomials in several variables
- 2-local triple homomorphisms on von Neumann algebras and JBW*-triples
- Zero subspaces of polynomials on \(\ell _1(\Gamma )\)
- Extremely non-complex \(C(K)\)spaces
- Extreme points in function algebras
- A characterization of maximal ideals
- Real Banach algebras
- A note on unitary operators in \(C^ *\)-algebras
- Real \(C^ *\)-algebras
- Homotopy type of linear groups of two classes of Banach spaces
- Complex methods, and the estimation of operator norms and spectra from real numerical ranges
- The linear polarization constant of \(\mathbb{R}^n\)
- Normed algebras
- A theorem on rings of operators
- Isometries of operator algebras
- A generalized Schwarz inequality and algebraic invariants for operator algebras
- A multiplicative Gleason-Kahane-Żelazko theorem for \(C^\star \)-algebras
- Zeros of real polynomials
- Sufficient conditions for a linear functional to be multiplicative
- Polynomial estimates on real and complex $L_p(\mu )$ spaces
- Lower bounds for norms of products of polynomials via Bombieri inequality
- Linear subsets of nonlinear sets in topological vector spaces
- Some applications of hypercontractive inequalities in quantum information theory
- Lineability
- THE COMPLEX PLANK PROBLEM
- Surjective isometries between real JB*-triples
- A survey on Tingley’s problem for operator algebras
- A proof that every Banach space is subreflexive
- Shorter Notes: An Elementary Proof of the Russo-Dye Theorem
- Contractive Projections on C 0 (K)
- Surjective Isometries of Real C -Algebras
- Bounds for the derivatives of polynomials on centrally symmetric convex bodies
- A Gleason-Kahane-Żelazko theorem for modules and applications to holomorphic function spaces
- V. A. Markov's theorems in normed spaces
- Complexification of the projective and injective tensor products
- Means of unitary operators, revisited
- The real plank problem and some applications
- Countable groups of isometries on Banach spaces
- A note on zeroes of real polynomials in $C(K)$ spaces
- Means and convex combinations of unitary operators.
- A Solution to the Invariant Subspace Problem on the Space l 1
- Contractive projections on Jordan $C^*$-algebras and generalizations.
- On the Existence and Uniqueness of Complex Structure and Spaces With "Few" Operators
- Real Isomorphic Complex Banach Spaces Need not be Complex Isomorphic
- A Superreflexive Banach Space Which Does Not Admit Complex Structure
- Weak*-continuity of Jordan triple products and its applications.
- On the definition of real 𝑊*-algebras
- Positive projections and Jordan structure in operator algebras.
- A characterization of multiplicative linear functionals in Banach algebras
- Lomonosov's hyperinvariant subspace theorem for real spaces
- When is a Linear Functional Multiplicative?
- Bounds on the derivatives of polynomials on Banach spaces
- Real Isometries between J B ∗ -Triples
- Weakly Compact Homomorphisms
- On Complex Strict and Uniform Convexity
- Banach Lattice Structures on Separable L p Spaces
- Orthonormal systems in Banach spaces and their applications
- Contractive projections in 𝐶₁ and 𝐶_{∞}
- A Vidav theorem for Banach Jordan algebras
- Lower Bounds for Norms of Products of Polynomials
- A Sharp Version of Mahler's Inequality for Products of Polynomials
- Real Banach Jordan Triples
- Three Problems in Search of a Measure
- Bohr’s power series theorem in several variables
- Local automorphisms and derivations on $\mathcal {B}(H)$
- A lower bound for the product of linear forms
- On the axiomatic definition of real JB*–triples
- PLANK PROBLEMS, POLARIZATION AND CHEBYSHEV CONSTANTS
- Geometric characterizations of some classes of operators in C*-algebras and von Neumann algebras
- On the linear polarization constants of finite dimensional spaces
- Non-Associative Normed Algebras
- Differentiability versus continuity: Restriction and extension theorems and monstrous examples
- A version of the Lomonosov invariant subspace theorem for real Banach spaces
- Extremal Multilinear Forms on Banach Spaces
- Weakly Compact Homomorphisms From C ∗ -Algebras are of Finite Rank
- Lower bounds for multilinear forms defined on Hilbert Spaces
- Bernstein and Markov-type inequalities for polynomials on real Banach spaces
- Lipschitz-free Banach spaces
- The group of automorphisms of L∞is algebraically reflexive
- Lineability and spaceability of sets of functions on $\mathbb {R}$
- An Elementary Example of a Banach Space not Isomorphic to its Complex Conjugate
- Complex convexity in Lebesgue-Bochner Function Spaces
- Structural Projections on JBW*-Triples
- Lower bounds for norms of products of polynomials on Lpspaces
- The polarization constant of finite dimensional complex spaces is one
- Asymmetric Choi–Davis inequalities
- MULTIPLICATIVE SPECTRAL FUNCTIONALS ON
- ON THE EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF A -TRIPLE AND A BANACH SPACE
- A SPHERICAL VERSION OF THE KOWALSKI–SŁODKOWSKI THEOREM AND ITS APPLICATIONS
- Mankiewicz’s theorem and the Mazur–Ulam property for $\mathbf {C}^*$-algebras
- Dirichlet Series and Holomorphic Functions in High Dimensions
- On the zero-set of 2-homogeneous polynomials in Banach spaces
- On the Extension Problems of Isometric and Nonexpansive Mappings
- Smooth analysis in Banach spaces
- Multiplicative maps into the spectrum
- Lower bounds for the constants in the Bohnenblust–Hille inequality: The case of real scalars
- Banach spaces whose algebras of operators have a large group of unitary elements
- 2-Local isometries and 2-local automorphisms on uniform algebras
- THE NORM OF THE PRODUCT OF POLYNOMIALS IN INFINITE DIMENSIONS
- Non-Associative Normed Algebras
- A lower bound on the radius of analyticity of a power series in a real Banach space
- Jordan algebras of self-adjoint operators
- Symmetry in Real Banach Spaces.
- A characterization of maximal ideals in commutative Banach algebras
- A characterization of multiplicative linear functionals in complex Banach algebras
- Analytic functions in Banach spaces
- Polynomials and multilinear mappings in topological vector-spaces
- Analytic functions in topological vector-spaces
- The Norm of a Hermitian Element in a Banach Algebra
- Characterisation of Isometries Between C*-Algebras
- A Vertex Property for Banach Algebras with Identity.
- Some remarks on polynomials
- A Theorem of the Hahn-Banach Type for Linear Transformations
- A Solution of the "Plank Problem"
- Banach Spaces with the Extension Property
- Complex Structures on Real Banach Spaces
- The Positive Cone in Banach Algebras
- Analytic operations in real Banach spaces
- Positive Functions on C ∗ -Algebras
- Matrix theory. Basic results and techniques
- Separably injective Banach spaces
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
