(A,m)-isometries on Hilbert spaces

Decomposing algebraic m-isometric tuples

“…It follows that an operator T is (A, m)-isometric if and only if T is m-isometric with respect to · A . As a result, several algebraic properties of (A, m)-isometries follow from the corresponding properties of m-isometries with more or less similar proofs (see [8,10]). However, there are great differences between (A, m)-isometries and m-isometries, specially when A is not injective.…”

“…Let A be a positive operator on H. An operator T is called an (A, m)isometry if it is a solution to the operator equation Such operators were introduced and studied by Sid Ahmed and Saddi in [8], then by other authors [17,25,29,23,19,10]. In the case m = 1, we call such operators A-isometries.…”

“…Such operators were introduced and studied by Sid Ahmed and Saddi in [8], then by other authors [17,25,29,23,19,10]. In the case m = 1, we call such operators A-isometries.…”

“…For example, it is known [5] that the spectrum of an m-isometry must either be a subset of the unit circle or the entire closed unit disk. On the other hand, [10,Theorem 2.3] shows that for any compact set K on the plane that intersects the unit circle, there exist a non-zero positive operator A and an (A, 1)-isometry whose spectrum is exactly K. The following question was asked in [10].…”

Functional models up to similarity and $a$-contractions

“…There are many papers on m-isometries for positive integers m. We can mention the works [6,7,8] by Bermúdez and coauthors, [12] by Gu,and [20] by Rydhe. In [17], more facts about 2-isometries are established.…”