For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...

Let A belong to the Schatten-von Neumann ideal Sp for 0 < p < ∞. We give an upper bound for the operator norm of the resolvent (zI − A)−1 of A in terms of the departure from normality of A and the distance of z to the spectrum of A. As an application we provide an upper bound for the Hausdorff distance of the spectra of two operators belonging to Sp.

Abstract. We generalize earlier results of [2], [3], [6], [13], [14] to the case of functions of n-tuples of commuting self-adjoint operators. In particular, we prove that if a function f belongs to the Besov space B ∞,1(R ), then f is operator Lipschitz and we show that if f satisfies a Hölder condition of order α, then ‖f(A1 · · · , An)− f(B1, · · · , Bn)‖ ≤ constmax1≤j≤n ‖Aj −Bj‖ α for all n...

Abstract It is well known that every $$l_2$$ l 2 -strictly singular operator from $$L_p$$ L p , $$1&lt;p&lt;\infty $$ 1 &lt; ∞ to any Banach space X with an uncon...

For a pair $$(A,B)$$ of not necessarily bounded and commuting self-adjoint operators for function f on the Euclidean space $${{\mathbb{R}}^{2}}$$ that belongs to inhomogeneous Besov class $$B_{{\infty ,1}}^{1}({{\mathbb{R}}^{2}})$$ , we define $$f(A,B)$$ these as densely defined operator. We consider problem estimating functions under perturbations . It is established if $$1 \leqslant p 2$$ $$(...

Two–sided estimates of Schatten–von Neumann norms for weighted Volterra integral operators are established. Analogous problems for some potential-type operators defined on R are solved. Let H be a separable Hilbert space and let σ∞(H) be the class of all compact operators T : H → H, which forms an ideal in the normed algebra B of all bounded linear operators onH. To construct a Schattenvon Neum...