Characteristic Functions of Two-Operator Vessels in a Hilbert Space

1995 ◽  
pp. 187-233
Author(s):  
M. S. Livšic ◽  
N. Kravitsky ◽  
A. S. Markus ◽  
V. Vinnikov
Keyword(s):  
Hilbert Space ◽  
Characteristic Functions

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.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space

A study the Spectrum for A Probabilistic Hilbert Space Operator

2017 ◽  
Vol 13 (3) ◽  
pp. 170-182
Author(s):  
Sarkesh Khalid Ridha ◽  
Keyword(s):  
Hilbert Space ◽  
Space Operator ◽  
Hilbert Space Operator

On Definition of Expansion Probabilistic Hilbert Space

2018 ◽  
Vol 14 (3) ◽  
pp. 59-73
Author(s):  
Ahmed Hasan Hamed ◽  
Keyword(s):  
Hilbert Space ◽  
Definition Of

ON A GENERALIZATION OF THE HILBERT SPACE

1989 ◽  
Vol 22 (1) ◽  
pp. 1-20
Author(s):  
Hubert Wywcki
Keyword(s):  
Hilbert Space
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