ﻻ يوجد ملخص باللغة العربية
A Banach space operator $Ain B({cal{X}})$ is polaroid, $Ain {cal{P}}$, if the isolated points of the spectrum $sigma(A)$ are poles of the operator; $A$ is hereditarily polaroid, $Ain{cal{HP}}$, if every restriction of $A$ to a closed invariant subspace is polaroid. Operators $Ain{cal{HP}}$ have SVEP on $Phi_{sf}(A)={lambda: A-lambda$ is semi Fredholm $}$: This, in answer to a question posed by Li and Zhou (Studia Math. 221(2014), 175-192), proves the necessity of the condition $Phi_{sf}^+(A)=emptyset$. A sufficient condition for $Ain B({cal{X}})$ to have SVEP on $Phi_{sf}(A)$ is that its component $Omega_a(A)={lambdainPhi_{sf}(A): rm{ind}(A-lambda)leq 0}$ is connected. We prove: If $Ain B({cal{H}})$ is a Hilbert space operator, then a necessary and sufficient condition for there to exist a compact operator $K$ such that $A+Kin{cal{HP}}$ is that $Omega_a(A)$ is connected.
A Banach space operator $Tin B(X)$ is left polaroid if for each $lambdainhbox{iso}sigma_a(T)$ there is an integer $d(lambda)$ such that asc $(T-lambda)=d(lambda)<infty$ and $(T-lambda)^{d(lambda)+1}X$ is closed; $T$ is finitely left polaroid if asc $
A pair of functions defined on a set X with values in a vector space E is said to be disjoint if at least one of the functions takes the value 0 at every point in X. An operator acting between vector-valued function spaces is disjointness preserving
A multiplicative Hankel operator is an operator with matrix representation $M(alpha) = {alpha(nm)}_{n,m=1}^infty$, where $alpha$ is the generating sequence of $M(alpha)$. Let $mathcal{M}$ and $mathcal{M}_0$ denote the spaces of bounded and compact mu
We introduce a mean counting function for Dirichlet series, which plays the same role in the function theory of Hardy spaces of Dirichlet series as the Nevanlinna counting function does in the classical theory. The existence of the mean counting func
We examine a variant of a Banach space $mathfrak{X}_{0,1}$ defined by Argyros, Beanland, and the second named author that has the property that it admits precisely two spreading models in every infinite dimensional subspace. We prove that this space