Title

Wandering vector multipliers for unitary groups

Authors

Authors

D. G. Han;D. Larson

Comments

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Abbreviated Journal Title

Trans. Am. Math. Soc.

Keywords

unitary system; wandering vector; wandering vector multiplier; von; Neumann algebra; wavelet system; Mathematics

Abstract

A wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system into itself. A special case of unitary system is a discrete unitary group. We prove that for many (and perhaps all) discrete unitary groups, the set of wandering vector multipliers is itself a group. We completely characterize the wandering vector multipliers for abelian and ICC unitary groups. Some characterizations of special wandering vector multipliers are obtained for other cases. In particular, there are simple characterizations for diagonal and permutation wandering vector multipliers. Similar results remain valid for irrational rotation unitary systems. We also obtain some results concerning the wandering vector multipliers for those unitary systems which are the ordered products of two unitary groups. There are applications to wavelet systems.

Journal Title

Transactions of the American Mathematical Society

Volume

353

Issue/Number

8

Publication Date

1-1-2001

Document Type

Article

Language

English

First Page

3347

Last Page

3370

WOS Identifier

WOS:000168753100014

ISSN

0002-9947

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