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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the infinite product of operators
in Hilbert space

Author: László Mate
Journal: Proc. Amer. Math. Soc. 126 (1998), 535-543
MSC (1991): Primary 47A05; Secondary 46C99, 15A60, 05C05
MathSciNet review: 1415333
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a necessary and sufficient condition for a certain set of infinite products of linear operators to be zero. We shall investigate also the case when this set of infinite products converges to a non-zero operator. The main device in these results is a weighted version of the König Lemma for infinite trees in graph theory.

References [Enhancements On Off] (What's this?)

  • [1] I. Daubechies and J. C. Lagarias, Sets of matrices all infinite product of which converge, Linear Algebra Appl. 161 (1992), 227-263. MR 93f:15006
  • [2] N. Dunford and J. Schwartz, Linear operators I, Interscience Publ., 1958. MR 22:8302
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Additional Information

László Mate
Affiliation: Institute of Mathematics, Technical University of Budapest, H-1111 Sztoczek u. 2 H 26, Budapest, Hungary

Keywords: Orthogonal decomposition, rooted tree, prefix, shift-invariant, joint spectral radius
Received by editor(s): May 15, 1996
Received by editor(s) in revised form: August 21, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society