Scalar-type spectral operators and holomorphie semigroups.
Selbstadjungierte Operatoren als ?dual" rein atomare Skalaroperatoren.
Separate and joint similarity to families of normal operators
Sets of bounded linear operators , ⊂ ℬ(H) (ℋ is a Hilbert space) are similar if there exists an invertible (in ℬ(H)) operator G such that . A bounded operator is scalar if it is similar to a normal operator. is jointly scalar if there exists a set ⊂ ℬ(H) of normal operators such that and are similar. is separately scalar if all its elements are scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented (Theorems...
Sequential closedness of Boolean algebras of projections in Banach spaces
Complete and σ-complete Boolean algebras of projections acting in a Banach space were introduced by W. Bade in the 1950's. A basic fact is that every complete Boolean algebra of projections is necessarily a closed set for the strong operator topology. Here we address the analogous question for σ-complete Boolean algebras: are they always a sequentially closed set for the strong operator topology? For the atomic case the answer is shown to be affirmative. For the general case, we develop criteria...
Simultaneous resolutions of the identity operator in normed spaces.
We construct in this paper some simultaneous projective resolutions of the identity operator which we later use to obtain certain new results on quasi-complementation property and Markushevich bases.
Sobolev- und Sobolev-Hardy-Räume auf S1: Dualitätstheorie und Funktionalkalküle.
Some properties of strongly -decomposable operators.
Some remarks on the surjectivity spectrum of linear operators
Some results on duality for spectral decompositions
Some spectral inequalities involving generalized scalar operators
In 1971, Allan Sinclair proved that for a hermitian element h of a Banach algebra and λ complex we have ∥λ + h∥ = r(λ + h), where r denotes the spectral radius. Using Levin's subordination theory for entire functions of exponential type, we extend this result locally to a much larger class of generalized spectral operators. This fundamental result improves many earlier results due to Gelfand, Hille, Colojoară-Foiaş, Vidav, Dowson, Dowson-Gillespie-Spain, Crabb-Spain, I. & V. Istrăţescu, Barnes,...
Spectral Decompositions and Decomposable Multipliers.
Spectral decompositions and harmonic analysis on UMD spaces
We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X.
Spectral decompositions, ergodic averages, and the Hilbert transform
Let U be a trigonometrically well-bounded operator on a Banach space , and denote by the sequence of (C,2) weighted discrete ergodic averages of U, that is, . We show that this sequence of weighted ergodic averages converges in the strong operator topology to an idempotent operator whose range is x ∈ : Ux = x, and whose null space is the closure of (I - U). This result expands the scope of the traditional Ergodic Theorem, and thereby serves as a link between Banach space spectral theory and...
Spectral decompositions in Banach spaces and the Hilbert transform
This paper gives a survey of some recent developments in the spectral theory of linear operators on Banach spaces in which the Hilbert transform and its abstract analogues play a fundamental role.
Spectral measures and automatic continuity.
Spectral projections, semigroups of operators, and the Laplace transform
Spectral Representation of Local Semigroups.
Spectral representation of local semigroups in locally convex spaces
Spectral Representations for Unbounded Operators with Real Spectrum.
Spectral theory and operator ergodic theory on super-reflexive Banach spaces
On reflexive spaces trigonometrically well-bounded operators have an operator-ergodic-theory characterization as the invertible operators U such that . (*) Trigonometrically well-bounded operators permeate many settings of modern analysis, and this note highlights the advances in both their spectral theory and operator ergodic theory made possible by a recent rekindling of interest in the R. C. James inequalities for super-reflexive spaces. When the James inequalities are combined with Young-Stieltjes...