The only continuous Volterra right inverses in of the operator are
The operator equation AX - XB = C with unbounded operators A and B and related abstract Cauchy problems.
The Operators Aγ = γA + -γA for a Class of Nondissipative Operators A with a Limit of the Corresponding Correlation Function
2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12In this work we present the operators Aγ = γA + -γA with Re γ = 1/2 in the case of an operator A from the class of nondissipative operators generating nonselfadjoint curves, whose correlation functions have a limit as t → ±∞. The asympthotics of the stationary curves e^(itAγ)f as t → ±∞ onto the absolutely continuous subspace of Aγ are obtained. These asymptotics and the obtained asymptotics in [9] of the nondissipative curves...
The Order on Projections in C*-Algebras of Real Rank Zero
We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of their lower bounds) decreasing sequences. Under the further assumption that the order is countably downwards closed, we show how to characterize greatest lower bounds of finite collections of projections, and their existence, using the norm and spectrum of simple...
The Ornstein-Uhlenbeck generator perturbed by the gradient of a potential
Si considera, in uno spazio di Hilbert l'operatore lineare , dove è un operatore negative autoaggiunto e è un potenziale che soddisfa a opportune condizioni di integrabilità. Si dimostra con un metodo analitico che è essenzialmente autoaggiunto in uno spazio e si caratterizza il dominio della sua chiusura come sottospazio di . Si studia inoltre la «spectral gap property» del semigruppo generato da .
The Perron-Frobenius theorem in relative spectral theory.
The pertubatively stable spectrum of a periodic Schrödinger operator.
The Polynomial-Normaloid Property for Banach-Space Operators
The Positive Supercyclicity Theorem.
We present some recent results related with supercyclic operators, also some of its consequences. We will finalize with new related questions.
The power boundedness and resolvent conditions for functions of the classical Volterra operator
Let ϕ(z) be an analytic function in a disk |z| < ρ (in particular, a polynomial) such that ϕ(0) = 1, ϕ(z)≢ 1. Let V be the operator of integration in , 1 ≤ p ≤ ∞. Then ϕ(V) is power bounded if and only if ϕ’(0) < 0 and p = 2. In this case some explicit upper bounds are given for the norms of ϕ(V)ⁿ and subsequent differences between the powers. It is shown that ϕ(V) never satisfies the Ritt condition but the Kreiss condition is satisfied if and only if ϕ’(0) < 0, at least in the polynomial...
The product of relatively regular operators
The pseudodifferential operator .
The ranges of nonlinear operators of the polynomial type
The rate of convergence of iterates of the Frobenius-Perron operator for piecewise monotonic transformations
The Regularized Trace for Nuclear Perturbations of Discrete Operators
The Relative Spectrum of Elements in a Real Banach Algebra.
The semigroup of Fredholm operators.
The single-point spectrum operators satisfying Ritt's resolvent condition
It is shown that an operator with the properties mentioned in the title does exist in the space , 1 ≤ p ≤ ∞. The maximal sector for the extended resolvent condition can be prescribed a priori jointly with the corresponding order of the exponential growth of the resolvent in the complementary sector.
The single-valued extension property and subharmonicity.
The single-valued extension property for sums and products of commuting operators
It is shown that the sum and the product of two commuting Banach space operators with Dunford’s property have the single-valued extension property.