Displaying similar documents to “Unbounded C * -seminorms, biweights, and * -representations of partial * -algebras: A review.”

Quasi *-algebras and generalized inductive limits of C*-algebras

Giorgia Bellomonte, Camillo Trapani (2011)

Studia Mathematica

Similarity:

A generalized procedure for the construction of the inductive limit of a family of C*-algebras is proposed. The outcome is no more a C*-algebra but, under certain assumptions, a locally convex quasi *-algebra, named a C*-inductive quasi *-algebra. The properties of positive functionals and representations of C*-inductive quasi *-algebras are investigated, in close connection with the corresponding properties of positive functionals and representations of the C*-algebras that generate...

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

Camillo Trapani (2005)

Banach Center Publications

Similarity:

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. ...

Peano-algebras and quasi-algebras

J. Słomiński

Similarity:

CONTENTSIntroduction.................................................................................................................... 5§ 1. Fundamental concepts for quasi-algebras..................................................... 5§ 2. Peano-algebras.................................................................................................... 13§ 3. Peano-algebras and free quasi-algebras....................................................... 25§ 4. Theorems concerning free...

A theory of extensions of quasi-algebras to algebras

J. Słomiński

Similarity:

CONTENTSINTRODUCTION...................................................................................................................................................................... 31. TERMS NOTATION AND LEMMAS.................................................................................................................................. 4A. Quasi-algebras and algebras..........................................................................................................................................................................

Bounded elements in certain topological partial *-algebras

Jean-Pierre Antoine, Camillo Trapani, Francesco Tschinke (2011)

Studia Mathematica

Similarity:

We continue our study of topological partial *-algebras, focusing on the interplay between various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between strong and weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *-algebras, emphasizing the crucial role played by appropriate bounded elements, called ℳ-bounded....

Locally convex quasi C*-algebras and noncommutative integration

Camillo Trapani, Salvatore Triolo (2015)

Studia Mathematica

Similarity:

We continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm topology and we focus our attention on the so-called locally convex quasi C*-algebras. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra (𝔛,𝔄₀) can be represented in a class of noncommutative local L²-spaces.