|
|
|
|
|
On the generalized
Calkin algebra
John J. Buoni and Albert Jonathan Klein |
|
Vol. 80 (1979), No. 1, 9–12
|
Abstract |
|
A bounded linear operation T : X → Y between Banach spaces is said to be weakly compact if it takes bounded sequences onto sequences which have a weakly convergent subsequence. Let W[X,Y ] denote the weakly compact operators from X to Y , B[X,Y ], the bounded operators and K[X,Y ], the compact operators. Now W[X,Y ] forms a closed subalgebra of B[X,Y ] and for X = Y , W[X,X] is a closed (in the uniform topology) two-sided ideal of B[X,X]. The purpose of this note is to construct a faithful representation of the Generalized Calkin Algebra B[X,X]∕K[X,X], which parallels a similar representation of B[X,X]∕K[X,X] in Buoni, Harte and Wickstead, “ Upper and lower Fredholm spectra”. |
Mathematical Subject Classification 2000
Primary: 47D30, 47D30
Secondary: 46H15
|
Milestones
Received: 5 April 1978
Revised: 14 July 1978
Published: 1 January 1979
|
Authors |
| John J. Buoni | |
| Albert Jonathan Klein | |
|
