Toral ( m , C ) $(m,C)$ -isometric multivariable operators
Abstract In recent years, various aspects of the problem related to the generalization of the class of m-isometries of commuting tuples of operators in Hilbert spaces have appeared in the literature. Let us mention, for example, ( n 1 , … , n p ) $(n_{1},\ldots ,n_{p})$ -quasi-m-isometric tuples, (...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03288-5 |
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| Summary: | Abstract In recent years, various aspects of the problem related to the generalization of the class of m-isometries of commuting tuples of operators in Hilbert spaces have appeared in the literature. Let us mention, for example, ( n 1 , … , n p ) $(n_{1},\ldots ,n_{p})$ -quasi-m-isometric tuples, ( m , C ) $(m,C)$ -isometric tuples, toral m-isometries, and toral ( m , A ) $(m, A)$ -isometries. In this paper, we discuss a problem closely related to this one. We introduce the class of toral- ( m , C ) $(m,C)$ -isometries for a tuple of commuting operators related to a given conjugation operator C on a Hilbert space H. We present its basic properties and demonstrate a variety of results that extend some works related to multivariable operators. |
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| ISSN: | 1029-242X |