Note on operators produced by sesquilinear forms
Note on pointwise contractive projections.
Note on the spectral inclusion theorem for Toeplitz operators
Note on the strong maximal operator
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 on commutator on the variable exponent Lebesgue spaces
We obtain the factorization theorem for Hardy space via the variable exponent Lebesgue spaces. As an application, it is proved that if the commutator of Coifman, Rochberg and Weiss is bounded on the variable exponent Lebesgue spaces, then is a bounded mean oscillation (BMO) function.
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 unbounded Toeplitz operators in Segal-Bargmann spaces
Relations between different extensions of Toeplitz operators are studied. Additive properties of closed Toeplitz operators are investigated, in particular necessary and sufficient conditions are given and some applications in case of Toeplitz operators with polynomial symbols are indicated.
Noyaux absolument mesurables ou basiques et opérateurs nucléaires
Noyaux associés à des opérateurs de Faraut
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.
Nuclear spaces of maximal diametral dimension
Numerical Algorithms for the Nevanlinna-Pick Problem.
Numerical index of vector-valued function spaces
We show that the numerical index of a -, -, or -sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.
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
It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained.
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.