An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space

2020 ◽  
Author(s):  
Konrad Schmüdgen
Keyword(s):  
Hilbert Space ◽  
Representations Of Algebras ◽  
Unbounded Representations

scholarly journals Unbounded representations of ∗-algebras

1977 ◽  
Vol 70 (2) ◽  
pp. 369-382 ◽  
Author(s):  
Stanley Gudder ◽  
W. Scruggs
Keyword(s):  
Representations Of Algebras ◽  
Unbounded Representations

Unitary equivalence of unbounded *-representations of *-algebras

1997 ◽  
Vol 122 (2) ◽  
pp. 269-279
Author(s):  
I. IKEDA ◽  
A. INOUE ◽  
M. TAKAKURA
Keyword(s):  
Von Neumann Algebras ◽  
Unitary Equivalence ◽  
Density Condition ◽  
Von Neumann ◽  
Representations Of Algebras ◽  
Unbounded Representations

In this paper the unitary equivalence of unbounded *-representations of *-algebras is investigated. It is shown that if closed *-representations π1 and π2 of a *-algebra [Ascr ] satisfy a certain density condition for the intertwining spaces [Jscr ](π1, π2) and [Jscr ](π2, π1), then a *-isomorphism Φ between the O*-algebras π1([Ascr ]) and π2([Ascr ]) is defined by Φ(π1(x))=π2(x), x∈[Ascr ] and it induces a *-isomorphism Φ¯, between the von Neumann algebras (π1([Ascr ])′w)′ and (π2([Ascr ])′w)′, and further if Φ¯, is spatial (that is, it is unitarily implemented), then π1 and π2 are unitarily equivalent.

Hilbert Space

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

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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