Publication details

A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms



Year of publication 2015
Type Article in Periodical
Magazine / Source International Journal of Theoretical Physics
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords Effect algebra; Generalized effect algebra; Hilbert space; Operator; Unbounded operator; Bilinear form; Singular bilinear form
Description The existence of a non-trivial singular positive bilinear form Simon (J. Funct. Analysis 28, 377-385 (1978)) yields that on an infinite-dimensional complex Hilbert space the set of bilinear forms is richer than the set of linear operators . We show that there exists an structure preserving embedding of partially ordered groups from the abelian po-group of symmetric bilinear forms with a fixed domain D on a Hilbert space into the po-group of linear symmetric operators on a dense linear subspace of an infinite dimensional complex Hilbert spacel (2)(M). Moreover, if we restrict ourselves to the positive parts of the above mentioned po-groups, we can embed positive bilinear forms into corresponding positive linear operators.

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