Automorphisms of linear semigroups over division rings.
Automorphisms of the algebra of operators in preserving conditioning
Let α be an isometric automorphism of the algebra of bounded linear operators in (p ≥ 1). Then α transforms conditional expectations into conditional expectations if and only if α is induced by a measure preserving isomorphism of [0, 1].
Automorphisms of the Loeb algebra
Auxiliary principle for generalized nonlinear variational-like inequalities.
Auxiliary principle for generalized strongly nonlinear mixed variational-like inequalities.
Averages of holomorphic mappings and holomorphic retractions on convex hyperbolic domains
Let D be a hyperbolic convex domain in a complex Banach space. Let the mapping F ∈ Hol(D,D) be bounded on each subset strictly inside D, and have a nonempty fixed point set ℱ in D. We consider several methods for constructing retractions onto ℱ under local assumptions of ergodic type. Furthermore, we study the asymptotic behavior of the Cesàro averages of one-parameter semigroups generated by holomorphic mappings.
Averages of unitary representations and weak mixing of random walks
Let S be a locally compact (σ-compact) group or semigroup, and let T(t) be a continuous representation of S by contractions in a Banach space X. For a regular probability μ on S, we study the convergence of the powers of the μ-average Ux = ʃ T(t)xdμ(t). Our main results for random walks on a group G are: (i) The following are equivalent for an adapted regular probability on G: μ is strictly aperiodic; converges weakly for every continuous unitary representation of G; U is weakly mixing for any...
Averaging in an ordinary differential equation.
Averaging theorems for linear operators in compact groups and semigroups
The Weyl criterion for uniform distribution of a sequence has an especially simple form in compact abelian groups. The authors use this and the structure of compact monothetic groups and semigroups to generalise the convergence, under certain compactness conditions, of the operator averages: where P is a projection associated with the eigenvalue one of T.
a-Weyl's theorem and perturbations
We study the stability of a-Weyl's theorem under perturbations by operators in some known classes. We establish in particular that if T is a finite a-isoloid operator, then a-Weyl's theorem is transmitted from T to T + R for every Riesz operator R commuting with T.
a-Weyl's theorem and the single valued extension property.
In the present paper, we study a-Weyl's and a-Browder's theorem for an operator T such that T or T* satisfies the single valued extension property (SVEP). We establish that if T* has the SVEP, then T obeys a-Weyl's theorem if and only if it obeys Weyl's theorem. Further, if T or T* has the SVEP, we show that the spectral mapping theorem holds for the essential approximative point spectrum, and that a-Browder's theorem is satisfied by f(T) whenever f ∈ H(σ(T)). We also provide several conditions...
Axiomatic theory of spectrum III: semiregularities
We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).
-bounded semigroups and implicit evolution equations.
-spaces and applications to extrapolation theory
We investigate a scale of -spaces defined with the help of certain Lorentz norms. The results are applied to extrapolation techniques concerning operators defined on adapted sequences. Our extrapolation works simultaneously with two operators, starts with --estimates, and arrives at --estimates, or more generally, at estimates between K-functionals from interpolation theory.
is generated in strong operator topology by two of its elements
Back to RS-SR spectral theory
Let X, Y be Banach spaces, S: X → Y and R: Y → X be bounded operators. We investigate common spectral properties of RS and SR. We then apply the result obtained to extensions, Aluthge transforms and upper triangular operator matrices.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Backward Aluthge iterates of a hyponormal operator and scalar extensions
Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar.
Backward Euler type methods for parabolic integro-differential equations in Banach space
Backward extensions of hyperexpansive operators
The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.