Vol. 80, No. 1, 1979

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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