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On the infinite product of operators in Hilbert space
Author(s):
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:
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:
- [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
- [3]
- D. Ruelle, Characteristic exponents and invariant manifolds in Hilbert space, Ann. Math. 115 (1982), 243-290. MR 83j:58097
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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
Email:
mate@math.bme.hu
DOI:
10.1090/S0002-9939-98-04067-2
PII:
S 0002-9939(98)04067-2
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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