Continuity of operators in spaces of vector functions, with applications to the theory of bases

DOI10.1007/BF01463181zbMath0666.46027MaRDI QIDQ1116411

A. V. Bukhvalov

Publication date: 1989

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

zbMATH Keywords

Orlicz spacesunconditional basesLorentz spacesrearrangement invariant Banach function spacesBanach spaces with unconditional martingale propertybases in the space E(X)

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of vector- and operator-valued functions (46E40) Linear operators on function spaces (general) (47B38) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items

Lipschitz continuity of the absolute value and Riesz projections in symmetric operator spaces ⋮ Narrow operators on tensor products of Köthe spaces ⋮ Contractibility of the linear group in Banach spaces of measurable operators

Cites Work

• Some remarks on Banach spaces in which martingale difference sequences are unconditional
• Extension of a result of Benedek, Calderón and Panzone
• Primarite de \(L^p(\ell_r),1<p,r<\infty\)
• Radon-Nikodym property in Banach spaces of measurable vector-functions
• Hardy spaces of vector-valued functions
• A geometrical characterization of Banach spaces in which martingale difference sequences are unconditional
• Primarité de \(L^ p(L^ r)\), \(1<p,r<\infty\)
• The Radon-Nikodym theorem for Lebesgue-Bochner function spaces
• On the existence of certain singular integrals
• Factorization Theory and A P Weights
• On the Basis Problem for Vector Valued Function Spaces
• On Singular Integrals
• Application of methods of the theory of order-bounded operators to the theory of operators inL^p-spaces
• Martingale Transforms and Complex Uniform Convexity
• A weighted norm inequality for singular integrals
• Unconditional bases and martingales in L_P(F)
• Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients
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