0000000000371456

AUTHOR

Jean Pierre Antoine

showing 2 related works from this author

Partial {$*$}-algebras of closable operators. I. The basic theory and the abelian case

1990

This paper, the first of two, is devoted to a systematic study of partial *-algebras of closable operators in a Hilbert space (partial Op*-algebras). After setting up the basic definitions, we describe canonical extensions of partial Op*-algebras by closure and introduce a new bounded commutant, called quasi-weak. We initiate a theory of abelian partial *-algebras. As an application, we analyze thoroughly the partial Op*-algebras generated by a single closed symmetric operator.

Semi-elliptic operatorAlgebraPure mathematicssymbols.namesakeGeneral MathematicsBounded functionClosure (topology)Hilbert spacesymbolsAbelian groupCentralizer and normalizerMathematicsSymmetric operatorPublications of the Research Institute for Mathematical Sciences
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Weak A-frames and weak A-semi-frames

2021

After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lower semi-frame controlled by a densely defined operator $A$ or, for short, a weak lower $A$-semi-frame and we study its properties. In particular, we compare it with that of lower atomic systems, introduced in (GB). We discuss duality properties and we suggest several possible definitions for weak $A$-upper semi-frames. Concrete examples are presented.

Numerical AnalysisPure mathematicsMatematikApplied MathematicsDensely defined operatorDuality (optimization)Functional Analysis (math.FA)41A99 42C15Mathematics - Functional AnalysisSettore MAT/05 - Analisi MatematicaA-frames weak (upper and lower) A-semi-frames lower atomic systems G-dualityFOS: MathematicsAnalysis$A$-framesweak (upper and lower) $A$-semi-frameslower atomic systems$G$-dualityMathematicsMathematics
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