(A, m)-partial isometries in semi-Hilbertian spaces,Linear and Multilinear Algebra

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(A, m)-partial isometries in semi-Hilbertian spaces
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2022-04-27 , DOI: 10.1080/03081087.2022.2068493
Adel Saddi ₁ , Fatma Mahmoudi ₁

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In this paper, we introduce the notion of $(A, m)$ -partial isometry for a positive operator A and a nonnegative integer m. This family of operators contains both the class of $(A, m)$ -isometries discussed in Sid Ahmed and Saddi [A-m-isometric operators in semi-Hilbertian spaces. Linear Algebra Appl. 2012;436:3930–3942] and that of m-partial isometries introduced in Saddi and Sid Ahmed [m-partial isometries on Hilbert spaces. Int J Funct Anal Oper Theory Appl. 2010;2(1):67–83]. First, we give some interesting algebraic properties of $(A, m)$ -partial isometries, then we discuss a necessary and sufficient condition for an $(A, m)$ -partial isometry to be an $(A, m)$ -isometry. Finally, we give some spectral properties of $(A, m)$ -partial isometries.

更新日期：2022-04-28

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