Some classes of topological quasi *-algebras

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Abstract

The completion A[τ] of a locally convex *-algebra A[τ] with not jointly continuous multiplication is a *-vector space with partial multiplication xy defined only for x or y ε A0, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ*-algebras and HCQ*-algebras are studied. Roughly speaking, a strict CQ*-algebra (resp. HCQ*-algebra) is a Banach (resp. Hubert) quasi *-algebra containing a C*-algebra endowed with another involution # and C*norm || ||#. HCQ*-algebras are closely related to left Hubert algebras. We shall show that a Hubert space is a HCQ*-algebra if and only if it contains a left Hubert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ*-aIgebra is embedded in a HCQ*-algebra. © 2001 American Mathematical Society.
Lingua originaleEnglish
pagine (da-a)2973-2980
Numero di pagine8
RivistaProceedings of the American Mathematical Society
Volume129
Stato di pubblicazionePublished - 2001

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Algebra
Class
Multiplication
Hubert Space
Stefan Banach
Vector spaces
Involution
C*-algebra
Vector space
Completion
Subspace
If and only if
Norm
Partial
Necessary Conditions
Unit

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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title = "Some classes of topological quasi *-algebras",
abstract = "The completion A[τ] of a locally convex *-algebra A[τ] with not jointly continuous multiplication is a *-vector space with partial multiplication xy defined only for x or y ε A0, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ*-algebras and HCQ*-algebras are studied. Roughly speaking, a strict CQ*-algebra (resp. HCQ*-algebra) is a Banach (resp. Hubert) quasi *-algebra containing a C*-algebra endowed with another involution # and C*norm || ||#. HCQ*-algebras are closely related to left Hubert algebras. We shall show that a Hubert space is a HCQ*-algebra if and only if it contains a left Hubert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ*-aIgebra is embedded in a HCQ*-algebra. {\circledC} 2001 American Mathematical Society.",
author = "Camillo Trapani and Fabio Bagarello and Inoue",
year = "2001",
language = "English",
volume = "129",
pages = "2973--2980",
journal = "Proceedings of the American Mathematical Society",
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TY - JOUR

T1 - Some classes of topological quasi *-algebras

AU - Trapani, Camillo

AU - Bagarello, Fabio

AU - Inoue, null

PY - 2001

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N2 - The completion A[τ] of a locally convex *-algebra A[τ] with not jointly continuous multiplication is a *-vector space with partial multiplication xy defined only for x or y ε A0, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ*-algebras and HCQ*-algebras are studied. Roughly speaking, a strict CQ*-algebra (resp. HCQ*-algebra) is a Banach (resp. Hubert) quasi *-algebra containing a C*-algebra endowed with another involution # and C*norm || ||#. HCQ*-algebras are closely related to left Hubert algebras. We shall show that a Hubert space is a HCQ*-algebra if and only if it contains a left Hubert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ*-aIgebra is embedded in a HCQ*-algebra. © 2001 American Mathematical Society.

AB - The completion A[τ] of a locally convex *-algebra A[τ] with not jointly continuous multiplication is a *-vector space with partial multiplication xy defined only for x or y ε A0, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ*-algebras and HCQ*-algebras are studied. Roughly speaking, a strict CQ*-algebra (resp. HCQ*-algebra) is a Banach (resp. Hubert) quasi *-algebra containing a C*-algebra endowed with another involution # and C*norm || ||#. HCQ*-algebras are closely related to left Hubert algebras. We shall show that a Hubert space is a HCQ*-algebra if and only if it contains a left Hubert algebra with unit as a dense subspace. Further, we shall give a necessary and sufficient condition under which a strict CQ*-aIgebra is embedded in a HCQ*-algebra. © 2001 American Mathematical Society.

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M3 - Article

VL - 129

SP - 2973

EP - 2980

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

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