Rajendra Bhatia, Driss Drissi (1999)
Studia Mathematica
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Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
Dina Štěrbová (1985)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Gaur, A.K. (1997)
International Journal of Mathematics and Mathematical Sciences
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Dina Štěrbová (1977)
Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika
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Maria Fragoulopoulou (2002)
Studia Mathematica
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A simple application of Pták theory for hermitian Banach algebras, combined with a result on normed Q-algebras, gives a non-technical new proof of the Shirali-Ford theorem. A version of this theorem in the setting of non-normed topological algebras is also provided.
Rachid ElHarti, Mohamed Mabrouk (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras...