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A New Seminorm for d -Tuples of A -Bounded Operators and Their Applications.
- Source :
- Mathematics (2227-7390); Feb2023, Vol. 11 Issue 3, p685, 21p
- Publication Year :
- 2023
-
Abstract
- The aim of this paper was to introduce and investigate a new seminorm of operator tuples on a complex Hilbert space H when an additional semi-inner product structure defined by a positive (semi-definite) operator A on H is considered. We prove the equality between this new seminorm and the well-known A-joint seminorm in the case of A-doubly-commuting tuples of A-hyponormal operators. This study is an extension of a well-known result in [Results Math 75, 93(2020)] and allows us to show that the following equalities r A (T) = ω A (T) = ∥ T ∥ A hold for every A-doubly-commuting d-tuple of A-hyponormal operators T = (T 1 , ... , T d) . Here, r A (T) , ∥ T ∥ A , and ω A (T) denote the A-joint spectral radius, the A-joint operator seminorm, and the A-joint numerical radius of T , respectively. [ABSTRACT FROM AUTHOR]
- Subjects :
- MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 161857449
- Full Text :
- https://doi.org/10.3390/math11030685