(m, C)-Isometric Toeplitz operators with rational symbols. Issue 19 (16th December 2022)

• Record Type: Journal Article
• Authors: Ko, Eungil; Lee, Ji Eun; Lee, Jongrak
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 19(2022)
• Page Start: 4360
• Page End: 4376
• Publication Date: 2022-12-16
• Subjects: (m, C)-isometric operators -- Toeplitz operators -- block Toeplitz operators; 47A05 -- 47A35 -- 47A62 -- 47B20; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1878997
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: An operator T ∈ L ( H ) is said to be ( m, C )-isometric if there exists a conjugation C such that 1 ∑ j = 0 m ( − 1 ) m − j ( m j ) T ∗ j C T j C = 0 for some positive integer m . In this paper, we study ( m, C )-isometric Toeplitz operators T φ with rational symbols φ . We characterize ( m, C )-isometric Toeplitz operators T φ by properties of the rational symbols φ . Moreover, we provide a concrete description of the ( m, C ) -isometric block Toeplitz operators.