We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.
Department of Mathematics and Computer Science, Georgia State University, Atlanta, Georgia 30303, U.S.A.
Bibliografia
[1] B. Aupetit, The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras, J. Funct. Anal. 47 (1982), 1-6.
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[3] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin 1973.
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[5] J. Esterle, Normes d'algèbres minimales, topologie d'algèbre normée minimum sur certaines algèbres d'endomorphismes continus d'un espace normé, C. R. Acad. Sci. Paris Sér. A 277 (1973), 425-427.
[6] M. J. Meyer, Minimal norms on SQDZ-Banach algebras, Proc. Roy. Irish Acad. 89A (1989), 127-133.
[7] M. J. Meyer, The spectral extension property and extension of multiplicative linear functionals, Proc. Amer. Math. Soc. 112 (1991), 855-861.
[8] T. W. Palmer, Spectral algebras, subalgebras and pseudonorms, Rocky Mountain J. Math., to appear.
[9] T. J. Ransford, A short proof of Johnson's theorem, Bull. London Math. Soc. 21 (1989), 487-488.
[10] C. E. Rickart, General Theory of Banach Algebras, Krieger, New York 1960.
[11] Á. Rodríguez-Palacios, Automatic continuity with application to C*-algebras, Math. Proc. Cambridge Philos. Soc., to appear.
[12] B. J. Tomiuk and B. Yood, Incomplete normed algebra norms on Banach algebras, Studia Math. 95 (1989), 119-132.
[13] B. Yood, Homomorphisms on normed algebras, Pacific J. Math. 8 (1958), 373-381.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv102i1p77bwm
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