Wandering vector multipliers for unitary groups

    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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