Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

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
Retrieve article in: PDF
This article is available free of charge

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:

[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

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A05, 46C99, 15A60, 05C05

Retrieve articles in all Journals with MSC (1991): 47A05, 46C99, 15A60, 05C05

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


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS