AN EXTREME POINT CRITERION FOR SEPARABILITY OF A DUAL BANACH SPACE, AND A NEW PROOF OF A THEOREM OF CORSON

1976 ◽  
Vol 27 (3) ◽  
pp. 379-385 ◽  
Author(s):  
RICHARD HAYDON
Keyword(s):  
Banach Space ◽  
Extreme Point ◽  
Dual Banach Space

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 < ∞.

Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces

2011 ◽  
Vol 54 (2) ◽  
pp. 515-529
Author(s):  
Philip G. Spain
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Boolean Algebras ◽  
C Algebra ◽  
C Algebras ◽  
Weak Star ◽  
Weakly Closed ◽  
Operator Closure ◽  
Dual Banach Space ◽  
Completion Theorem

AbstractPalmer has shown that those hermitians in the weak-star operator closure of a commutative C*-algebra represented on a dual Banach space X that are known to commute with the initial C*-algebra form the real part of a weakly closed C*-algebra on X. Relying on a result of Murphy, it is shown in this paper that this last proviso may be dropped, and that the weak-star closure is even a W*-algebra.When the dual Banach space X is separable, one can prove a similar result for C*-equivalent algebras, via a ‘separable patch’ completion theorem for Boolean algebras of projections on such spaces.

Biholomorphic Mappings on Banach Spaces

2019 ◽  
Vol 62 (4) ◽  
pp. 913-924
Author(s):  
H. Carrión ◽  
P. Galindo ◽  
M. L. Lourenço
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Open Subset ◽  
Separable Hilbert Space ◽  
Derivative Operator ◽  
Infinite Dimensional ◽  
Dimensional Version ◽  
Dual Banach Space ◽  
Bounded Convex ◽  
Power Bounded

AbstractWe present an infinite-dimensional version of Cartan's theorem concerning the existence of a holomorphic inverse of a given holomorphic self-map of a bounded convex open subset of a dual Banach space. No separability is assumed, contrary to previous analogous results. The main assumption is that the derivative operator is power bounded, and which we, in turn, show to be diagonalizable in some cases, like the separable Hilbert space.

scholarly journals Strongly Extreme Points and Approximation Properties

2018 ◽  
Vol 61 (3) ◽  
pp. 449-457
Author(s):  
Trond A. Abrahamsen ◽  
Petr Hájek ◽  
Olav Nygaard ◽  
Stanimir L. Troyanski
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Extreme Point ◽  
Convex Subset ◽  
Approximation Property ◽  
Extreme Points ◽  
Local Approximation ◽  
Approximation Properties ◽  
Compact Approximation ◽  
Approximation Of The Identity

AbstractWe show that if x is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approximation at x, then x is already a denting point. It turns out that such an approximation of the identity exists at any strongly extreme point of the unit ball of a Banach space with the unconditional compact approximation property. We also prove that every Banach space with a Schauder basis can be equivalently renormed to satisfy the suõcient conditions mentioned.

scholarly journals To what extent does the dual Banach space E′ determine the polynomials over E?

2000 ◽  
Vol 38 (2) ◽  
pp. 343-354 ◽  
Author(s):  
Silvia Lassalle ◽  
Ignacio Zalduendo
Keyword(s):  
Banach Space ◽  
Dual Banach Space

scholarly journals The states of a Banach algebra generate the dual

1971 ◽  
Vol 17 (4) ◽  
pp. 341-344 ◽  
Author(s):  
Allan M. Sinclair
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Linear Combination ◽  
Linear Functional ◽  
Measure Theory ◽  
Complex Field ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
Unital Banach Algebra ◽  
Dual Banach Space

In this paper we prove that the states of a unital Banach algebra generate the dual Banach space as a linear space (Theorem 2). This is a result of R. T. Moore (4, Theorem 1(a)) who uses a decomposition of measures in his proof. In the proof given here the measure theory is replaced by a Hahn-Banach separation argument. We shall let A denote a unital Banach algebra over the complex field, and D(1) denote {f ∈ A′: ‖f‖ = f(1) = 1} where A′ is the dual of A. The motivation of Moore's results is the theorem that in a C*-algebra every continuous linear functional is a linear combination of four states (the states are the elements of D(1)) (see (2, 2.6.4, 2.1.9, 1.1.10)).

On the Duality of Operator Spaces

1995 ◽  
Vol 38 (3) ◽  
pp. 334-346 ◽  
Author(s):  
Christian Le Merdy
Keyword(s):  
Banach Space ◽  
Von Neumann Algebras ◽  
Related Result ◽  
Space Structure ◽  
Operator Space ◽  
Operator Spaces ◽  
Bounded Operators ◽  
Von Neumann ◽  
Operator Space Structure ◽  
Dual Banach Space

AbstractWe prove that given an operator space structure on a dual Banach space Y*, it is not necessarily the dual one of some operator space structure on Y. This allows us to show that Sakai's theorem providing the identification between C*-algebras having a predual and von Neumann algebras does not extend to the category of operator spaces. We also include a related result about completely bounded operators from B(ℓ2)* into the operator Hilbert space OH.

A Banach–Stone theorem for spaces of weak* continuous functions

1985 ◽  
Vol 101 (3-4) ◽  
pp. 203-206 ◽  
Author(s):  
Michael Cambern
Keyword(s):  
Banach Space ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Hausdorff Spaces ◽  
Space Of Continuous Functions ◽  
Dual Banach Space ◽  
Stone Theorem

SynopsisIf X is a compact Hausdorff space and E a dual Banach space, let C(X, Eσ*) denote the Banach space of continuous functions F from X to E when the latter space is provided with its weak * topology, normed by . It is shown that if X and Y are extremally disconnected compact Hausdorff spaces and E is a uniformly convex Banach space, then the existence of an isometry between C(X, Eσ*) and C(Y, Eσ*) implies that X and Y are homeomorphic.

scholarly journals Completely positive linear operators for Banach spaces

1994 ◽  
Vol 17 (1) ◽  
pp. 27-30
Author(s):  
Mingze Yang
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Banach Spaces ◽  
Extreme Point ◽  
General Setting ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Complete Positivity ◽  
Completely Positive

Using ideas of Pisier, the concept of complete positivity is generalized in a different direction in this paper, where the Hilbert spaceℋis replaced with a Banach space and its conjugate linear dual. The extreme point results of Arveson are reformulated in this more general setting.

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