Displaying similar documents to “On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space”

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...

Quasi-multipliers of the algebra of approximable operators and its duals

Michael Grosser (1997)

Studia Mathematica

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Let A be the Banach algebra K 0 ( X ) of approximable operators on an arbitrary Banach space X. For the spaces of all bilinear continuous quasi-multipliers of A resp. its dual A* resp. its bidual A**, concrete representations as spaces of operators are given.

On the semi-Browder spectrum

Vladimír Kordula, Vladimír Müller, Vladimir Rakočević (1997)

Studia Mathematica

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An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators.

Factorization through Hilbert space and the dilation of L(X,Y)-valued measures

V. Mandrekar, P. Richard (1993)

Studia Mathematica

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We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.

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E. Albrecht, W. Ricker (1998)

Studia Mathematica

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The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in L p ( ℝ N ) . The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi:...

Measures and lacunary sets

Pascal Lefèvre (1999)

Studia Mathematica

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We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.

Calderón-Zygmund operators and unconditional bases of weighted Hardy spaces

J. García-Cuerva, K. Kazarian (1994)

Studia Mathematica

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We study sufficient conditions on the weight w, in terms of membership in the A p classes, for the spline wavelet systems to be unconditional bases of the weighted space H p ( w ) . The main tool to obtain these results is a very simple theory of regular Calderón-Zygmund operators.