Operators and Quadratic Forms in Hilbert Space

2018 ◽  
pp. 115-158
Author(s):  
David E. Edmunds ◽  
W. Desmond Evans
Keyword(s):  
Hilbert Space ◽  
Quadratic Forms

Conditional Positivity of Quadratic Forms in Hilbert Space

1980 ◽  
Vol 11 (6) ◽  
pp. 1047-1057 ◽  
Author(s):  
D. H. Martin
Keyword(s):  
Hilbert Space ◽  
Quadratic Forms

Lower semicontinuhy of positive quadratic forms

1978 ◽  
Vol 79 (3-4) ◽  
pp. 267-273 ◽  
Author(s):  
Barry Simon
Keyword(s):  
Hilbert Space ◽  
Lower Semicontinuity ◽  
Quadratic Forms

SynopsisWe develop various facets of the theory of quadratic forms on a Hilbert space suggested by a criterion of Kato which characterizes closed forms in terms of lower semicontinuity.

scholarly journals Schwartz operators

2016 ◽  
Vol 28 (03) ◽  
pp. 1630001 ◽  
Author(s):  
M. Keyl ◽  
J. Kiukas ◽  
R. F. Werner
Keyword(s):  
Hilbert Space ◽  
Harmonic Analysis ◽  
Quadratic Forms ◽  
Moment Problems ◽  
Space Operator ◽  
Convergence Properties ◽  
Unbounded Operators ◽  
Tempered Distributions ◽  
New Methods ◽  
Schwartz Functions

In this paper, we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them, in particular, with a number of different (but equivalent) families of seminorms which turns the space of Schwartz operators into a Fréchet space. The study of the topological dual leads to non-commutative tempered distributions which are discussed in detail as well. We show, in particular, that the latter can be identified with a certain class of quadratic forms, therefore making operations like products with bounded (and also some unbounded) operators and quantum harmonic analysis available to objects which are otherwise too singular for being a Hilbert space operator. Finally, we show how the new methods can be applied by studying operator moment problems and convergence properties of fluctuation operators.

Hilbert Space

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