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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.
For a principal type pseudodifferential operator, we prove that condition 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 for any (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition doesnotimply local solvability with a loss of 1 derivative,...
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.
In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions.
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