On joint spectra of operators on a Banach space isomorphic to its square
One computes the joint and essential joint spectra of a pair of multiplication operators with bounded analytic functions on the Hardy spaces of the unit ball in .
An exactness lemma offers a simplified account of the spectral properties of the "holomorphic" analogue of normal solvability.
This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of th order with complex coefficients , provided that all th quasi-derivatives of solutions of and all solutions of its normal adjoint are in and under suitable conditions on the function .
A recurrence relation for the computation of the -norms of an Hermitian Fredholm integral operator is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of this operator an a priori and an a posteriori bound for the error are obtained. Some properties of the a posteriori bound are discussed.
We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.
In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp , where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.