Displaying similar documents to “On a theorem of Toeplitz”

Theory of the integral

Stanisław Saks

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CONTENTS PREFACE...................... III ERRATA.......................... VII CHAPTER I. The integral in an abstract space § 1. Introduction.................................. 1 § 2. Terminology and notation...................... 4 § 3. Abstract space X.............................. 6 § 4. Additive classes of sets...................... 7 § 5. Additive functions of a set................... 8 § 6. The variations of an additive function........ 10 § 7. Measurable functions.............................

On a theorem of Gelfand and its local generalizations

Driss Drissi (1997)

Studia Mathematica

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In 1941, I. Gelfand proved that if a is a doubly power-bounded element of a Banach algebra A such that Sp(a) = 1, then a = 1. In [4], this result has been extended locally to a larger class of operators. In this note, we first give some quantitative local extensions of Gelfand-Hille’s results. Secondly, using the Bernstein inequality for multivariable functions, we give short and elementary proofs of two extensions of Gelfand’s theorem for m commuting bounded operators, T 1 , . . . , T m , on a Banach...