Banach ideals of p-compact operators

1979 ◽  
Vol 26 (4) ◽  
pp. 349-362 ◽  
Author(s):  
Jan Fourie ◽  
Johan Swart
2013 ◽  
Vol 397 (2) ◽  
pp. 628-643 ◽  
Author(s):  
A.F. Ber ◽  
V.I. Chilin ◽  
G.B. Levitina ◽  
F.A. Sukochev

2008 ◽  
Vol 103 (1) ◽  
pp. 130
Author(s):  
J. M. Delgado ◽  
C. Piñeiro

We characterize Banach ideals $[\mathcal{A},a]$ satisfying the equality $c_0(\mathcal{A}(X,Y))= \mathcal{A}(X,c_0(Y))$ for all Banach spaces $X$ and $Y$. Among other results we have proved that $\mathcal{K}$ (the normed operator ideal of all compact operators with the operator norm) is the only injective Banach ideal satisfying the equality.


1981 ◽  
Vol 35 (3) ◽  
pp. 343-351 ◽  
Author(s):  
Jan H. Fourie ◽  
Johan Swart

1990 ◽  
Vol 13 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Hans G. Feichtinger ◽  
A. Turan Gürkanli

Continuing a line of research initiated by Larsen, Liu and Wang [12], Martin and Yap [13], Gürkanli [15], and influenced by Reiter's presentation of Beurling and Segal algebras in Reiter [2,10] this paper presents the study of a family of Banach ideals of Beurling algebrasLw1(G),Ga locally compact Abelian group. These spaces are defined by weightedLp-conditions of their Fourier transforms. In the first section invariance properties and asymptotic estimates for the translation and modulation operators are given. Using these it is possible to characterize inclusions in section 3 and to show that two spaces of this type coincide if and only if their parameters are equal. In section 4 the existence of approximate identities in these algebras is established, from which, among other consequences, the bijection between the closed ideals of these algebras and those of the corresponding Beurling algebra is derived.


2007 ◽  
Vol 14 (4) ◽  
pp. 807-808
Author(s):  
Giorgi Oniani

Abstract Corrections to [Oniani, Georgian Math. J. 13: 501–514, 2006] are listed.


2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ahmed Morsy ◽  
Nashat Faried ◽  
Samy A. Harisa ◽  
Kottakkaran Sooppy Nisar

AbstractIn this work, we establish an approach to constructing compact operators between arbitrary infinite-dimensional Banach spaces without a Schauder basis. For this purpose, we use a countable number of basic sequences for the sake of verifying the result of Morrell and Retherford. We also use a nuclear operator, represented as an infinite-dimensional matrix defined over the space $\ell _{1}$ℓ1 of all absolutely summable sequences. Examples of nuclear operators over the space $\ell _{1}$ℓ1 are given and used to construct operators over general Banach spaces with specific approximation numbers.


1991 ◽  
Vol 34 (2) ◽  
pp. 260-264 ◽  
Author(s):  
M. Radjabalipour

AbstractIf A is a norm closed algebra of compact operators on a Hilbert space and if its Jacobson radical J(A) consists of all quasinilpotent operators in A then A/ J(A) is commutative. The result is not valid for a general algebra of polynomially compact operators.


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