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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/11477
Title: Analytic m-isometries without the wandering subspace property
Authors: Trivedi, Shailesh
Keywords: Mathematics
Isometries
Issue Date: 2020
Publisher: AMS
Abstract: The wandering subspace problem for an analytic norm-increasing -isometry on a Hilbert space asks whether every -invariant subspace of can be generated by a wandering subspace. An affirmative solution to this problem for is ascribed to Beurling-Lax-Halmos, while that for is due to Richter. In this paper, we capitalize on the idea of weighted shift on a one-circuit directed graph to construct a family of analytic cyclic -isometries which do not admit the wandering subspace property and which are norm-increasing on the orthogonal complement of a one-dimensional space. Further, on this one-dimensional space, their norms can be made arbitrarily close to . We also show that if the wandering subspace property fails for an analytic norm-increasing -isometry, then it fails miserably in the sense that the smallest -invariant subspace generated by the wandering subspace is of infinite codimension.
URI: https://www.ams.org/journals/proc/2020-148-05/S0002-9939-2020-14894-0/home.html
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11477
Appears in Collections:Department of Mathematics

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