On polynomially partial--isometric operators

MA Aouichaoui, D Mosic - Turkish Journal of Mathematics, 2023 - journals.tubitak.gov.tr
MA Aouichaoui, D Mosic
Turkish Journal of Mathematics, 2023journals.tubitak.gov.tr
This paper presents a generalization of the concepts of partial-$ A $-isometry and left
polynomially partial isometry. Our investigation is inspired by previous work in the field [5,
30, 31]. By extending the definition of partial-$ A $-isometry, we provide new insights into the
properties and applications of these mathematical objects. In particular, we define the notion
of left $ p $-partial-$ A $-isometry as a broader class of operators, including partial-$ A $-
isometry and left polynomially partial isometry. Some basic properties of a left $ p $-partial …
Abstract
This paper presents a generalization of the concepts of partial--isometry and left polynomially partial isometry. Our investigation is inspired by previous work in the field [5, 30, 31]. By extending the definition of partial--isometry, we provide new insights into the properties and applications of these mathematical objects. In particular, we define the notion of left -partial--isometry as a broader class of operators, including partial--isometry and left polynomially partial isometry. Some basic properties of a left -partial--isometry are proven, as well as its relation with -isometry. Several decompositions of a left -partial--isometry are developed. We consider spectral properties and matrix representation of left -partial--isometries. Additionally, we provide some applications of left -partial--isometries.
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