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Invariant subspace lattices of Lambert's weighted shifts

Part of: General theory of linear operators Individual linear operators as elements of algebraic systems Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

B. S. Yadav  and
S. Chatterjee
B. S. Yadav
Affiliation:
Department of Mathematics University of DelhiDelhi-110007, India
S. Chatterjee
Affiliation:
Department of Mathematics University of DelhiDelhi-110007, India
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Abstract

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Let B(H) be the Banach algebra of all (bounded linear) operators on an infinite-dimensional separable complex Hilbert space H and let be a bounded sequence of positive real numbers. For a given injective operator A in B(H) and a non-zero vector f in H, we put We define a weighted shift Tw with the weight sequence on the Hilbert space 12 of all square-summable complex sequences by . The main object of this paper is to characterize the invariant subspace lattice of Tw under various nice conditions on the operator A and the sequence .

MSC classification

Secondary: 47A15: Invariant subspaces 47B99: None of the above, but in this section 47C05: Operators in algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 135 - 142
Copyright
Copyright © Australian Mathematical Society 1982

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