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1
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Bounded elements and spectrum in Banach quasi *-algebras

100%
Trapani C.
Studia Mathematica
|
2006
|
tom 172
|
nr 3
249-273
EN
A normal Banach quasi *-algebra (𝔛,) has a distinguished Banach *-algebra $𝔛_{b}$ consisting of bounded elements of 𝔛. The latter *-algebra is shown to coincide with the set of elements of 𝔛 having finite spectral radius. If the family 𝓟(𝔛) of bounded invariant positive sesquilinear forms on 𝔛 contains sufficiently many elements then the Banach *-algebra of bounded elements can be characterized via a C*-seminorm defined by the elements of 𝓟(𝔛).
2
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C*-seminorms on partial *-algebras: an overview

100%
Trapani C.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
369-384
EN
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.
3
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*-Representations, seminorms and structure properties of normed quasi *-algebras

100%
Trapani C.
Studia Mathematica
|
2008
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tom 186
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nr 1
47-75
EN
The class of *-representations of a normed quasi *-algebra (𝔛,𝓐₀) is investigated, mainly for its relationship with the structure of (𝔛,𝓐₀). The starting point of this analysis is the construction of GNS-like *-representations of a quasi *-algebra (𝔛,𝓐₀) defined by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms defines some seminorms (in some cases, C*-seminorms) that provide useful information on the structure of (𝔛,𝓐₀) and on the continuity properties of its *-representations.
4
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Erratum/Addendum to the paper "Some seminorms on quasi *-algebras" (Studia Math. 158 (2003), 99-115)

100%
Trapani C.
Studia Mathematica
|
2004
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tom 160
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nr 1
101
5
Content available remote

Some seminorms on quasi *-algebras

100%
Trapani C.
Studia Mathematica
|
2003
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tom 158
|
nr 2
99-115
EN
Different types of seminorms on a quasi *-algebra (𝔄,𝔄₀) are constructed from a suitable family ℱ of sesquilinear forms on 𝔄. Two particular classes, extended C*-seminorms and CQ*-seminorms, are studied in some detail. A necessary and sufficient condition for the admissibility of a sesquilinear form in terms of extended C*-seminorms on (𝔄,𝔄₀) is given.
6
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Erratum/addendum to the paper: "Quasi *-algebras and generalized inductive limits of C*-algebras" (Studia Math. 202 (2011), 165-190)

64%
Bellomonte G., Trapani C.
Studia Mathematica
|
2013
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tom 217
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nr 1
95-96
7
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Representations of modules over a *-algebra and related seminorms

64%
Trapani C., Triolo S.
Studia Mathematica
|
2008
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tom 184
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nr 2
133-148
EN
Representations of a module 𝔛 over a *-algebra $𝔄_{#}$ are considered and some related seminorms are constructed and studied, with the aim of finding bounded *-representations of $𝔄_{#}$.
8
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Locally convex quasi C*-algebras and noncommutative integration

64%
Trapani C., Triolo S.
Studia Mathematica
|
2015
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tom 228
|
nr 1
33-45
EN
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.
9
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Quasi *-algebras and generalized inductive limits of C*-algebras

64%
Bellomonte G., Trapani C.
Studia Mathematica
|
2011
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tom 202
|
nr 2
165-190
EN
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 the structure. The typical example of the quasi *-algebra of operators acting on a rigged Hilbert space is analyzed in detail.
10
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Quasi *-algebras of measurable operators

51%
Bagarello F., Trapani C., Triolo S.
Studia Mathematica
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2006
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tom 172
|
nr 3
289-305
EN
Non-commutative $L^{p}$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (𝔛,𝔄₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.
11
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Bounded elements in certain topological partial *-algebras

51%
Antoine J.-P., Trapani C., Tschinke F.
Studia Mathematica
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2011
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tom 203
|
nr 3
223-251
EN
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. Finally, some remarks are made concerning representations in terms of so-called partial GC*-algebras of operators.
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