Norm inequalities in star algebras.
Norm inequalities relating singular integrals and the maximal function
Norm of a derivation and hyponormal operators.
Normal extensions of commutative subnormal operators
Norms of certain operators on weighted spaces and Lorentz sequence spaces.
Norms of certain rational functions of a matrix and Schur's criterion for polynomials
Norms of hypercyclic sequences.
Norms of inverses, spectra, and pseudospectra of large truncated Wiener-Hopf operators and Toeplitz matrices.
Note on a Paper of T. Lezanski Concerning ΄΄Almost Reciprocal Operations΄΄
Note on operational quantities and Mil'man isometry spectrum.
Let X and Y be infinite dimensional Banach spaces and let L(X,Y) be the class of all (linear continuous) operators acting between X and Y. Mil'man [5] introduced the isometry spectrum I(T) of T ∈ L(X,Y) in the following way:I(T) = {α ≥ 0: ∀ ε > 0, ∃M ∈ S∞(X), ∀x ∈ SM, | ||Tx|| - α | < ε}},where S∞(X) is the set of all infinite dimensional closed subspaces of X and SM := {x ∈ M: ||x|| = 1} is the unit sphere of M ∈ S∞(X). (...)
Note on operators produced by sesquilinear forms
Note on the spectral inclusion theorem for Toeplitz operators
Note to the paper by R. Hempel, A. M. Hinz, and H. Kalf: On the Essential Spectrum of Schrödinger Operators with Spherically Symmetric Potentials.
Notes about the hypercyclicity criterion
Notes on q-deformed operators
The paper concerns operators of deformed structure like q-normal and q-hyponormal operators with the deformation parameter q being a positive number different from 1. In particular, an example of a q-hyponormal operator with empty spectrum is given, and q-hyponormality is characterized in terms of some operator inequalities.
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.
Notes on the Taylor joint spectrum of commuting operators
n-supercyclic and strongly n-supercyclic operators in finite dimensions
We prove that on , there is no n-supercyclic operator with 1 ≤ n < ⌊(N + 1)/2⌋, i.e. if has an n-dimensional subspace whose orbit under is dense in , then n is greater than ⌊(N + 1)/2⌋. Moreover, this value is optimal. We then consider the case of strongly n-supercyclic operators. An operator is strongly n-supercyclic if has an n-dimensional subspace whose orbit under T is dense in , the nth Grassmannian. We prove that strong n-supercyclicity does not occur non-trivially in finite...
n-supercyclic operators
We show that there are linear operators on Hilbert space that have n-dimensional subspaces with dense orbit, but no (n-1)-dimensional subspaces with dense orbit. This leads to a new class of operators, called the n-supercyclic operators. We show that many cohyponormal operators are n-supercyclic. Furthermore, we prove that for an n-supercyclic operator, there are n circles centered at the origin such that every component of the spectrum must intersect one of these circles.
N-th roots of a non-negative operator: conditions for uniqueness.