Characterization of Banach space through validity of Bochner theorem

1978 ◽  
pp. 314-326 ◽  
Author(s):  
V. Mandrekar
Keyword(s):  
Banach Space ◽  
Bochner Theorem

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

scholarly journals Decompositions of Weakly Compact Valued Integrable Multifunctions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 863 ◽  
Author(s):  
Luisa Di Piazza ◽  
Kazimierz Musiał
Keyword(s):  
Banach Space ◽  
Separable Banach Space ◽  
Compact Convex ◽  
Weakly Compact ◽  
Seminal Paper ◽  
Decomposition Property ◽  
Short Overview ◽  
Decomposition Theorems ◽  
State Of Art

We give a short overview on the decomposition property for integrable multifunctions, i.e., when an “integrable in a certain sense” multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it starting from the seminal paper of the authors in 2006, where the property was proved for Henstock integrable multifunctions taking compact convex values in a separable Banach space X. In this paper, we summarize the earlier results, we prove further results and present tables which show the state of art in this topic.

scholarly journals Complex extreme measurable selections

1995 ◽  
Vol 58 (2) ◽  
pp. 222-231
Author(s):  
Douglas Mupasiri
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Extreme Point ◽  
Measure Space ◽  
Sufficient Conditions ◽  
Complex Banach Space ◽  
Closed Unit Ball ◽  
Measurable Selections ◽  
Necessary And Sufficient

AbstractWe give a characterization of complex extreme measurable selections for a suitable set-valued map. We use this result to obtain necessary and sufficient conditions for a function to be a complex extreme point of the closed unit ball of Lp (ω, Σ, ν X), where (ω, σ, ν) is any positive, complete measure space, X is a separable complex Banach space, and 0 < p < ∞.

A New Characterization of Hardy Martingale Cotype Space

2004 ◽  
Vol 47 (4) ◽  
pp. 481-491
Author(s):  
Turdebek N. Bekjan
Keyword(s):  
Banach Space ◽  
Best Constants ◽  
Plurisubharmonic Functions ◽  
Martingale Inequalities ◽  
Martingale Cotype

AbstractWe give a new characterization of Hardy martingale cotype property of complex quasi- Banach space by using the existence of a kind of plurisubharmonic functions. We also characterize the best constants of Hardy martingale inequalities with values in the complex quasi-Banach space.

A characterization of M-Summands

1974 ◽  
Vol 76 (1) ◽  
pp. 157-159 ◽  
Author(s):  
Richard Evans
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Closed Subspace ◽  
Structure Theory ◽  
Linear Projection ◽  
Image Position

In the structure theory of Banach spaces as developed in (1), an important role is played by subspaces which are the ranges of projections having norm properties akin to those of the classical Banach spaces. A linear projection e on a Banach space V is called an M-projection ifand an L-projection if, insteadA closed subspace J of V is called an M-Summand if it is the range of an M-projection and an M-Ideal if J0 is the range of an L-projection in V′. Every M-Summand is an M-Ideal but the reverse is false.

scholarly journals A characterization of the essential pseudospectra on a Banach space

2013 ◽  
Vol 2 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Banach Space

scholarly journals THE HILLE–YOSIDA THEOREM FOR LOCAL CONVOLUTED SEMIGROUPS

2003 ◽  
Vol 46 (2) ◽  
pp. 395-413 ◽  
Author(s):  
Valentin Keyantuo ◽  
Claus Müller ◽  
Peter Vieten
Keyword(s):  
Banach Space ◽  
Laplace Transform ◽  
Characterization Theorem ◽  
Real Variable ◽  
Subject Classification ◽  
Exponential Case ◽  
Primary 47D03 ◽  
Convoluted Semigroups

AbstractThe characterization theorem for the Banach-space-valued local Laplace transform established by Keyantuo, Müller and Vieten is used to obtain a real variable characterization of generators of local convoluted semigroups. The concept of local convoluted semigroups extends that of distribution as well as ultradistribution semigroups. Complete characterizations existed only for exponentially bounded semigroups integrated $\alpha$ times, whereas for the non-exponential case generation results had been obtained in terms of complex conditions only.AMS 2000 Mathematics subject classification: Primary 47D03; 47D06; 44A10

scholarly journals A SPECTRAL CHARACTERIZATION OF OPERATORS

2016 ◽  
Vol 102 (3) ◽  
pp. 369-391 ◽  
Author(s):  
SATISH K. PANDEY ◽  
VERN I. PAULSEN
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Real Banach Space ◽  
Closed Subspace ◽  
Characterization Theorem ◽  
Positive Operators ◽  
Spectral Characterization ◽  
Proper Cone ◽  
Arbitrary Dimensions

We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless, we prove that the intersection of these operators with the positive operators forms a proper cone in the real Banach space of hermitian operators.

scholarly journals Wavelets Convergence and Unconditional Bases for Lp(ℝn) and H1(ℝn)

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Banach Space ◽  
Hardy Space ◽  
Function Space ◽  
Riesz Transform ◽  
Unconditional Bases

We prove that reasonable nice wavelets form unconditional bases in function space other than L2(ℝn, X). Moreover, characterization of convergence of wavelets series in Lp(ℝn, X) space and Hardy space H1(ℝn,X) has been obtained. Here, X is a Banach space with boundedness of Riesz transform.

Sign in / Sign up

Export Citation Format

Share Document