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-$A$-isometry are proven, as well as its relation with $A$-isometry. Several decompositions of a left $p$-partial-$A$-isometry are developed. We consider spectral properties and matrix representation of left $p$-partial-$A$-isometries. Additionally, we provide some applications of left $p$-partial-$A$-isometries.
Partial isometry, $A$-isometry, semi-inner product, spectrum
AOUICHAOUI, MOHAMED AMINE and MOSIC, DIJANA
"On polynomially partial-$A$-isometric operators,"
Turkish Journal of Mathematics: Vol. 47:
7, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss7/18