Sup-norm-closable bilinear forms and Lagrangians
| Autor: | Michael Hinz |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Pure mathematics Symmetric bilinear form Dirichlet form Sesquilinear form Mathematics::Operator Algebras Applied Mathematics 010102 general mathematics Spectrum (functional analysis) Bilinear form Mathematics::Spectral Theory 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis 010104 statistics & probability Uniform norm Bounded function 28A25 46A05 46E05 47A07 FOS: Mathematics Locally compact space 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1407.1301 |
| Popis: | We consider symmetric non-negative definite bilinear forms on algebras of bounded real valued functions and investigate closability with respect to the supremum norm. In particular, any Dirichlet form gives rise to a sup-norm closable bilinear form. Under mild conditions a sup-norm closable bilinear form admits finitely additive energy measures. If, in addition, there exists a (countably additive) energy dominant measure, then a sup-norm closable bilinear form can be turned into a Dirichlet form admitting a carr\'e du champ. Moreover, we can always transfer the bilinear form to an isometrically isomorphic algebra of bounded functions on the Gelfand spectrum, where these measures exist. Our results complement a former closability study of Mokobodzki for the locally compact and separable case. |
| Databáze: | OpenAIRE |
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