Separating vectors for operators

    Authors

    D. Han; D. Larson; Z. Pan;W. Wogen

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    separating vector; extension of operators; triangular operator; integral; domain; EXTENSIONS; REFLEXIVITY; ALGEBRAS; Mathematics, Applied; Mathematics

    Abstract

    It is an open problem whether every one-dimensional extension of a triangular operator admits a separating vector. We prove that the answer is positive for many triangular Hilbert space operators, and in particular, for strictly triangular operators. This is revealing, because two-dimensional extensions of such operators can fail to have separating vectors.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    135

    Issue/Number

    3

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    713

    Last Page

    723

    WOS Identifier

    WOS:000242238300012

    ISSN

    0002-9939

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