Hyperstonean cover and second dual extension

1988 ◽  
Vol 51 (1-2) ◽  
pp. 125-149 ◽  
Author(s):  
V. K. Zaharov
Keyword(s):  
Second Dual ◽  
Dual Extension

scholarly journals Module amenability of the second dual and module topological center of semigroup algebras

2010 ◽  
Vol 80 (2) ◽  
pp. 302-312 ◽  
Author(s):  
Massoud Amini ◽  
Abasalt Bodaghi ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Semigroup Algebras ◽  
Topological Center ◽  
Module Amenability ◽  
Second Dual

scholarly journals ON A WEAKLY UNIFORMLY ROTUND DUAL OF A BANACH SPACE

2012 ◽  
Vol 92 (1) ◽  
Author(s):  
J. R. GILES
Keyword(s):  
Banach Space ◽  
Second Dual

Every Banach space with separable second dual can be equivalently renormed to have weakly uniformly rotund dual. Under certain embedding conditions a Banach space with weakly uniformly rotund dual is reflexive.

A General Construction of Spaces of the Type of R. C. James

1975 ◽  
Vol 27 (6) ◽  
pp. 1263-1270 ◽  
Author(s):  
Robert H. Lohman ◽  
Peter G. Casazza
Keyword(s):  
Banach Space ◽  
General Construction ◽  
Finite Codimension ◽  
Reflexive Space ◽  
Second Dual

In 1950, R. C. James [7] exhibited a nonreflexive Banach space with a basis that is of finite codimension in its second dual. This space is the first example of a quasi-reflexive space. General results on quasi-reflexive spaces have been obtained by P. Civin and B. Yood [3], and quasi-reflexive spaces with bases have been studied by D. Dean, B. L. Lin, and I. Singer [4 ; 12].

scholarly journals The second dual of C0 (S, A)

1994 ◽  
Vol 56 (3) ◽  
pp. 303-313
Author(s):  
Stephen T. L. Choy ◽  
James C. S. Wong
Keyword(s):  
Function Space ◽  
Simple Proof ◽  
Representation Theorem ◽  
Generalized Functions ◽  
Arens Product ◽  
Nikodym Property ◽  
Second Dual ◽  
Vector Valued Function ◽  
Vector Valued

AbstractThe second dual of the vector-valued function space C0(S, A) is characterized in terms of generalized functions in the case where A* and A** have the Radon-Nikodým property. As an application we present a simple proof that C0 (S, A) is Arens regular if and only if A is Arens regular in this case. A representation theorem of the measure μh is given, where , h ∈ L∞ (|μ;|, A**) and μh is defined by the Arens product.

scholarly journals First two bilateral hand transplantations in India (Part 3): Rehabilitation and immediate outcome

2017 ◽  
Vol 50 (02) ◽  
pp. 161-167
Author(s):  
Mohit Sharma ◽  
Subramania Iyer ◽  
P. Kishore ◽  
Jimmy Mathew ◽  
Sundeep Vijayaraghavan ◽  
...  
Keyword(s):  
Management Strategies ◽  
Standard Of Care ◽  
Daily Basis ◽  
Substantial Improvement ◽  
Outcome Analysis ◽  
Functional Magnetic Resonance ◽  
Experimental Procedure ◽  
Management Protocol ◽  
Second Dual

ABSTRACT Introduction: This report covers the strategies adopted for rehabilitation for the first and second dual hand transplants performed in India. Materials and Methods: The team, under a trained physiatrist, including physiotherapy and occupational therapy personnel, was involved in the management of both these patients. The management protocol was developed considering previous reports as well as our management strategies in the rehabilitation of the replanted hands. The involvement of the team with the patients started in the 1st week itself and continued on a daily basis for the entire year. Results: Outcome analysis was performed at 6 months and 1 year using the disability of shoulder and hand evaluation and hand transplant scoring system. Functional magnetic resonance imaging was done at the end of 1 year to assess the cortical integration of the transplanted hand. Conclusion: Despite more than 110 hands being transplanted worldwide, hand transplant remains an experimental procedure. It is still not considered the “standard of care” for hand amputees. Outcome analyses performed worldwide do indicate that the procedure can provide a substantial improvement in the quality of life for the hand amputee, especially the bilateral amputees.

Johnson pseudo-contractibility of second duals of certain Banach algebras

2019 ◽  
pp. 2150012
Author(s):  
A. Sahami ◽  
E. Ghaderi ◽  
S. M. Kazemi Torbaghan ◽  
B. Olfatian Gillan
Keyword(s):  
Tensor Product ◽  
Matrix Algebra ◽  
Banach Algebras ◽  
Amenable Group ◽  
Semigroup Algebra ◽  
Archimedean Semigroup ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
The Matrix ◽  
Second Dual

In this paper, we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is a finite amenable group, where [Formula: see text] is an archimedean semigroup. We also show that the matrix algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is finite. We study Johnson pseudo-contractibility of certain projective tensor product second duals Banach algebras.

Ideals of the Quantum Group Algebra, Arens Regularity and Weakly Compact Multipliers

2020 ◽  
Vol 63 (4) ◽  
pp. 825-836
Author(s):  
Mehdi Nemati ◽  
Maryam Rajaei Rizi
Keyword(s):  
Quantum Group ◽  
Group Algebra ◽  
Approximate Identity ◽  
Compact Quantum Group ◽  
Closed Ideal ◽  
Locally Compact ◽  
Weakly Compact ◽  
Locally Compact Quantum Group ◽  
Arens Regularity ◽  
Second Dual

AbstractLet $\mathbb{G}$ be a locally compact quantum group and let $I$ be a closed ideal of $L^{1}(\mathbb{G})$ with $y|_{I}\neq 0$ for some $y\in \text{sp}(L^{1}(\mathbb{G}))$. In this paper, we give a characterization for compactness of $\mathbb{G}$ in terms of the existence of a weakly compact left or right multiplier $T$ on $I$ with $T(f)(y|_{I})\neq 0$ for some $f\in I$. Using this, we prove that $I$ is an ideal in its second dual if and only if $\mathbb{G}$ is compact. We also study Arens regularity of $I$ whenever it has a bounded left approximate identity. Finally, we obtain some characterizations for amenability of $\mathbb{G}$ in terms of the existence of some $I$-module homomorphisms on $I^{\ast \ast }$ and on $I^{\ast }$.

scholarly journals Complemented subspaces ofp-adic second dual Banach spaces

1995 ◽  
Vol 18 (3) ◽  
pp. 437-442
Author(s):  
Takemitsu Kiyosawa
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Complemented Subspaces ◽  
Complete Field ◽  
Second Dual

LetKbe a non-archimedean non-trivially valued complete field. In this paper we study Banach spaces overK. Some of main results are as follows: (1) The Banach spaceBC((l∞)1)has an orthocomplemented subspace linearly homeomorphic toc0. (2) The Banach spaceBC((c0)1)has an orthocomplemented subspace linearly homeomorphic tol∞.

Amenability of Banach algebras

1989 ◽  
Vol 105 (2) ◽  
pp. 351-355 ◽  
Author(s):  
Frédéric Gourdeau
Keyword(s):  
Banach Algebra ◽  
Metric Space ◽  
Banach Algebras ◽  
Approximate Identity ◽  
Commutative Banach Algebra ◽  
Cohomology Theory ◽  
Compact Metric Space ◽  
Amenable Banach Algebra ◽  
Second Dual

We consider the problem of amenability for a commutative Banach algebra. The question of amenability for a Banach algebra was first studied by B. E. Johnson in 1972, in [5]. The most recent contributions, to our knowledge, are papers by Bade, Curtis and Dales [1], and by Curtis and Loy [3]. In the first, amenability for Lipschitz algebras on a compact metric space K is studied. Using the fact, which they prove, that LipαK is isometrically isomorphic to the second dual of lipαK, for 0 < α < 1, they show that lipαK is not amenable when K is infinite and 0 < α < 1. In the second paper, the authors prove, without using any serious cohomology theory, some results proved earlier by Khelemskii and Scheinberg [8] using cohomology. They also discuss the amenability of Lipschitz algebras, using the result that a weakly complemented closed two-sided ideal in an amenable Banach algebra has a bounded approximate identity. Their result is stronger than that of [1].

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