Generalized coresolvents of aH-isometric operator with unequal defect numbers

1972 ◽  
Vol 5 (4) ◽  
pp. 329-331 ◽  
Author(s):  
G. K. Langer
Keyword(s):  
Isometric Operator

On n-quasi-m-isometric operators

2016 ◽  
Vol 09 (04) ◽  
pp. 1650073 ◽  
Author(s):  
Salah Mecheri ◽  
T. Prasad
Keyword(s):  
Hilbert Space ◽  
Matrix Representation ◽  
Isometric Operator ◽  
Basic Properties

We introduce the class of [Formula: see text]-quasi-[Formula: see text]-isometric operators on Hilbert space. This generalizes the class of [Formula: see text]-isometric operators on Hilbert space introduced by Agler and Stankus. An operator [Formula: see text] is said to be [Formula: see text]-quasi-[Formula: see text]-isometric if [Formula: see text] In this paper [Formula: see text] matrix representation of a [Formula: see text]-quasi-[Formula: see text]-isometric operator is given. Using this representation we establish some basic properties of this class of operators.

scholarly journals (m, p)-isometric and (m, ∞)-isometric operator tuples on normed spaces

2015 ◽  
Vol 08 (02) ◽  
pp. 1550022 ◽  
Author(s):  
Philipp H. W. Hoffmann ◽  
Michael Mackey
Keyword(s):  
Hilbert Spaces ◽  
Normed Spaces ◽  
Isometric Operator ◽  
Natural Way

We generalize the notion of m-isometric operator tuples on Hilbert spaces in a natural way to operator tuples on normed spaces. This is done by defining a tuple analogue of (m, p)-isometric operators, so-called (m, p)-isometric operator tuples. We then extend this definition further by introducing (m, ∞)-isometric operator tuples and study properties of and relations between these objects.

scholarly journals Unitary Boundary Pairs for Isometric Operators in Pontryagin Spaces and Generalized Coresolvents

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
D. Baidiuk ◽  
V. Derkach ◽  
S. Hassi
Keyword(s):  
Hilbert Space ◽  
Schur Functions ◽  
Characteristic Functions ◽  
General Notion ◽  
Pontryagin Space ◽  
Isometric Operator ◽  
Pontryagin Spaces ◽  
Alternative Approach ◽  
Boundary Triple ◽  
Space Case

AbstractAn isometric operator V in a Pontryagin space $${{{\mathfrak {H}}}}$$ H is called standard, if its domain and the range are nondegenerate subspaces in $${{{\mathfrak {H}}}}$$ H . A description of coresolvents for standard isometric operators is known and basic underlying concepts that appear in the literature are unitary colligations and characteristic functions. In the present paper generalized coresolvents of non-standard Pontryagin space isometric operators are described. The methods used in this paper rely on a new general notion of boundary pairs introduced for isometric operators in a Pontryagin space setting. Even in the Hilbert space case this notion generalizes the earlier concept of boundary triples for isometric operators and offers an alternative approach to study operator valued Schur functions without any additional invertibility requirements appearing in the ordinary boundary triple approach.

scholarly journals The properties of [∞,C]-isometric operators

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4541-4548
Author(s):  
Junli Shen ◽  
Kun Yu ◽  
Alatancang Chen
Keyword(s):  
Isometric Operator ◽  
Nilpotent Operator

In this paper we introduce the class of [?,C]-isometric operators and study various properties of this class. In particular, we show that if T is an [?,C]-isometric operator and Q is a quasi-nilpotent operator, then T + Q is an [?,C]-isometric operator under suitable conditions. Also, we show that the class of [?,C]-isometric operators is norm closed. Finally, we examine properties of products of [?,C]-isometric operators.

scholarly journals On an elementary operator with 2-isometric operator entries

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5083-5088 ◽  
Author(s):  
Junli Shen ◽  
Guoxing Ji
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Space Operator ◽  
Connected Component ◽  
Elementary Operator ◽  
Isometric Operator ◽  
Hilbert Space Operator

A Hilbert space operator T is said to be a 2-isometric operator if T*2T2- 2T*T + I = 0. Let dAB ? B(B(H)) denote either the generalized derivation ?AB = LA-RB or the elementary operator ?= LARB-I, we show that if A and B* are 2-isometric operators, then, for all complex ?, (dAB-?)-1(0)? (d*AB-?)-1(0), the ascent of (dAB-?) ? 1, and dis polaroid. Let H(?(dAB)) denote the space of functions which are analytic on ?(dAB), and let Hc(?(dAB)) denote the space of f ? H(?(dAB)) which are non-constant on every connected component of ?(dAB), it is proved that if A and B* are 2-isometric operators, then f(dAB) satisfies the generalized Weyl?s theorem and f(d*AB) satisfies the generalized a-Weyl?s theorem.

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