Möbius transformations and monogenic functional calculus.
Modal stabilizability and spectral synthesis
Multidimensional weak resolvents and spatial equivalence of normal operators
The aim of this paper is to answer some questions concerning weak resolvents. Firstly, we investigate the domain of extension of weak resolvents Ω and find a formula linking Ω with the Taylor spectrum. We also show that equality of weak resolvents of operator tuples A and B results in isomorphism of the algebras generated by these operators. Although this isomorphism need not be of the form (1) X ↦ U*XU, where U is an isometry, for normal operators it is always possible...
Multiplicity theory
Normal extensions of commutative subnormal operators
Normal operators spaces of distributions.
Notes on some spectral radius and numerical radius inequalities
We prove numerical radius inequalities for products, commutators, anticommutators, and sums of Hilbert space operators. A spectral radius inequality for sums of commuting operators is also given. Our results improve earlier well-known results.
N-th roots of a non-negative operator: conditions for uniqueness.
Numerical radius and operator norm inequalities.
Numerical radius inequalities for 2 × 2 operator matrices
We derive several numerical radius inequalities for 2 × 2 operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.
Numerical radius inequalities for Hilbert space operators. II
We give several sharp inequalities involving powers of the numerical radii and the usual operator norms of Hilbert space operators. These inequalities, which are based on some classical convexity inequalities for nonnegative real numbers and some operator inequalities, generalize earlier numerical radius inequalities.
On a binary relation between normal operators
The main goal of this paper is to clarify the antisymmetric nature of a binary relation ≪ which is defined for normal operators A and B by: A ≪ B if there exists an operator T such that for all Borel subset Δ of the complex plane ℂ, where and are spectral measures of A and B, respectively (the operators A and B are allowed to act in different complex Hilbert spaces). It is proved that if A ≪ B and B ≪ A, then A and B are unitarily equivalent, which shows that the relation ≪ is a partial order...
On a Class of Normaloid Operators.
On a function that realizes the maximal spectral type
We show that for a unitary operator U on , where X is a compact manifold of class , , and μ is a finite Borel measure on X, there exists a function that realizes the maximal spectral type of U.
On a Functional Which is Quadratic on A-orthogonal Vectors
On a generalization of Lumer-Phillips' theorem for dissipative operators in a Banach space
Using [1], which is a local generalization of Gelfand's result for powerbounded operators, we first give a quantitative local extension of Lumer-Philips' result that states conditions under which a quasi-nilpotent dissipative operator vanishes. Secondly, we also improve Lumer-Phillips' theorem on strongly continuous semigroups of contraction operators.
On a theorem of Gelfand and its local generalizations
In 1941, I. Gelfand proved that if a is a doubly power-bounded element of a Banach algebra A such that Sp(a) = 1, then a = 1. In [4], this result has been extended locally to a larger class of operators. In this note, we first give some quantitative local extensions of Gelfand-Hille’s results. Secondly, using the Bernstein inequality for multivariable functions, we give short and elementary proofs of two extensions of Gelfand’s theorem for m commuting bounded operators, , on a Banach space X.
On a Weyl-von Neumann type theorem for antilinear self-adjoint operators
Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators is constructed....
On an abstract evolution equation with a spectral operator of scalar type.
On an integral representation of antisymmetric operations in Hilbert spaces. I. Bounded operations