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Transitive Vector Spaces of Bounded Operators

Published online by Cambridge University Press:  20 November 2018

Sandy Grabiner
Sandy Grabiner*
Affiliation:
Department of Mathematics, Pomona College, Claremont, California, 91711
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Abstract

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The linear subspace S of B(X, Y), the space of bounded operators from the Banach space X to the Banach space Y, is said to be transitive if Sx is dense in Y for all x ≠ 0. We give a number of conditions, involving operators intertwined by S, which imply that S is not transitive, and conditions which, when X = Y, imply that the commutant of S is also not transitive.

Keywords

47A1547D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 381 - 384
Copyright
Copyright © Canadian Mathematical Society 1984

References

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