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ALGEBRA HOMOMORPHISMS FROM REAL WEIGHTED $L^1$ ALGEBRAS

Published online by Cambridge University Press:  08 January 2008

Pedro J. Miana
Pedro J. Miana
Affiliation:
Department of Mathematics, Universidad de Zaragoza, C/Pedro Cerbuna, 12-50009 Zaragoza, Spain (pjmiana@unizar.es)
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Abstract

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We characterize algebra homomorphisms from the Lebesgue algebra $L^1_\omega(\mathbb{R})$ into a Banach algebra $\mathcal{A}$. As a consequence of this result, every bounded algebra homomorphism $\varPhi:L^1_\omega(\mathbb{R})\to\mathcal{A}$ is approached through a uniformly bounded family of fractional homomorphisms, and the Hille–Yosida theorem for $C_0$-groups is proved.

Keywords

Primary 44A1047D62Secondary 26A3346J25pseudo-resolventsalgebra homomorphismsWeyl fractional calculusintegrated groups
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 725 - 735
Copyright
Copyright © Edinburgh Mathematical Society 2007