Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Characterizations of $ w\sp{\ast} $-homomorphisms and expectations


Author: T. W. Palmer
Journal: Proc. Amer. Math. Soc. 46 (1974), 265-272
MSC: Primary 46K99
MathSciNet review: 0361804
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ \mathfrak{A}$ and $ \mathfrak{B}$ are $ \ast $-algebras a map $ \phi :\mathfrak{A} \to \mathfrak{B}$ is called a Schwarz map if it is linear and satisfies the Cauchy-Schwarz inequality $ \phi {(a)^ \ast }\phi (a) \leq \phi (a ^\ast a)$ for all $ a \in \mathfrak{A}$. Under mild restrictions on $ \mathfrak{A}$ and $ \mathfrak{B}$, $ \ast $-homomorphisms and expectations are characterized in terms of Schwarz maps $ \phi :\mathfrak{A} \to \mathfrak{B}$. The proofs are based on an elementary result on the multiplicative properties of Schwarz maps.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46K99

Retrieve articles in all journals with MSC: 46K99


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0361804-1
PII: S 0002-9939(1974)0361804-1
Keywords: $ \ast $-algebra, $ \ast $-homomorphism, Cauchy-Schwarz inequality, expectation, Banach $ \ast $-algebra, $ {U^ \ast }$-algebra, Jordan $ \ast $-homomorphism
Article copyright: © Copyright 1974 American Mathematical Society