ISOMETRIC PAIRS WITH COMPACT + NORMAL CROSS-COMMUTATOR

作     者：De, Sandipan Sarkar, Jaydeb Shankar, P. Sankar, T.R. 

作者机构：School of Mathematics and Computer Science Indian Institute of Technology Goa Ponda Goa Farmagudi403401 India Indian Statistical Institute Statistics and Mathematics Unit 8th Mile Mysore Road Bangalore560 059 India Department of Mathematics Cochin University of Science and Technology Kerala Kochi682022 India 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

摘      要：We represent and classify pairs of commuting isometries (V1, V2) acting on Hilbert spaces that satisfy the condition [V1∗, V2] = compact + normal, where [V1∗, V2]:= V1∗V2 − V2V1∗ is the cross-commutator of (V1, V2). The precise description of such pairs also gives a complete and concrete set of unitary invariants. The basic building blocks of representations of such pairs consist of four distinguished pairs of commuting isometries. One of them relies on some peculiar examples of invariant subspaces tracing back to Rudin’s intricate constructions of analytic functions on the bidisc. Along the way, we present a rank formula for a general pair of commuting isometries that looks to be the first of its *** Codes 47A15, 32A10, 42B30, 47A13, 30H10, 47A65, 46E30, 47B47, 15A15 Copyright © 2024, The Authors. All rights reserved.