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C*-seminorms on partial *-algebras: an overview

Camillo Trapani (2005)

Banach Center Publications

The main facts about unbounded C*-seminorms on partial *-algebras are reviewed and the link with the representation theory is discussed. In particular, starting from the more familiar case of *-algebras, we examine C*-seminorms that are defined from suitable families of positive linear or sesquilinear forms, mimicking the construction of the Gelfand seminorm for Banach *-algebras. The admissibility of these forms in terms of the (unbounded) C*-seminorms they generate is characterized.

Cutting the loss of derivatives for solvability under condition ( Ψ )

Nicolas Lerner (2006)

Bulletin de la Société Mathématique de France

For a principal type pseudodifferential operator, we prove that condition  ( ψ ) implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from ϵ + 3 / 2 for any ϵ > 0 (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition  ( ψ ) doesnotimply local solvability with a loss of 1 derivative,...

Cyclic space isomorphism of unitary operators

Krzysztof Frączek (1997)

Studia Mathematica

We introduce a new equivalence relation between unitary operators on separable Hilbert spaces and discuss a possibility to have in each equivalence class a measure-preserving transformation.

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