Multipliers of mixed-norm sequence spaces and measures of noncompactness.
Multipliers of spaces of derivatives
For subspaces, and , of the space, , of all derivatives denotes the set of all such that for all . Subspaces of are defined depending on a parameter . In Section 6, is determined for each of these subspaces and in Section 7, is found for and any of these subspaces. In Section 3, is determined for other spaces of functions on related to continuity and higher order differentiation.
Multipliers of weighted spaces
Necessary and sufficient conditions for the boundedness of Dunkl-type fractional maximal operator in the Dunkl-type Morrey spaces.
New equivalent conditions for Hardy-type inequalities
We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant. The findings are crucial in the study of oscillation and non-oscillation properties of differential equation solutions, as well as spectral properties.
Nontrivial isometries on alpha).
Nonwandering operators in Banach space.
Norms of certain operators on weighted spaces and Lorentz sequence spaces.
Numerical range of operators acting on Banach spaces
The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small...
On a problem of Kadison and Singer.
On a weighted Toeplitz operator and its commutant.
On an infinite-dimensional version of the Kreiss matrix theorem
On bases and the shift operator
On Bernstein type rational functions of two variables
On convexity of composition and multiplication operators on weighted Hardy spaces.
On cyclicity in weighted Dirichlet spaces.
On extended eigenvalues and extended eigenvectors of truncated shift
In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..
On matrix transformations concerning the Nakano vector-valued sequence space.
On norm closed ideals in
It is well known that the only proper non-trivial norm closed ideal in the algebra L(X) for (1 ≤ p < ∞) or X = c₀ is the ideal of compact operators. The next natural question is to describe all closed ideals of for 1 ≤ p,q < ∞, p ≠ q, or equivalently, the closed ideals in for p < q. This paper shows that for 1 < p < 2 < q < ∞ there are at least four distinct proper closed ideals in , including one that has not been studied before. The proofs use various methods from Banach...
On some BK spaces.