Open AccessGleason‐kahane‐Żelazko theorem for spectrally bounded algebra
Author(s) -
S. H. Kulkarni,
D. Sukumar
Publication year - 2005
Publication title -
international journal of mathematics and mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 39
eISSN - 1687-0425
pISSN - 0161-1712
DOI - 10.1155/ijmms.2005.2447
Subject(s) - mathematics , bounded function , spectrum (functional analysis) , invertible matrix , multiplicative function , linear map , generalization , element (criminal law) , pure mathematics , algebra over a field , discrete mathematics , mathematical analysis , physics , quantum mechanics , political science , law
We prove by elementary methods the following generalization of a theorem due to Gleason, Kahane, and Żelazko. Let A be a real algebra with unit 1 such that the spectrum of every element in A is bounded and let φ:A→ℂ be a linear map such that φ(1)=1 and (φ(a))2
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