اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCompact and weakly compact disjointness preserving operators on spaces of differentiable functions
184
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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 if it maps disjoint functions to disjoint functions. We characterize compact and weakly compact disjointness preserving operators between spaces of Banach space-valued differentiable functions.
قيم البحث
اقرأ أيضاً
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
ltiplicative Hankel operators, respectively. In this note it is shown that the distance from an operator $M(alpha) in mathcal{M}$ to the compact operators is minimized by a nonunique compact multiplicative Hankel operator $N(beta) in mathcal{M}_0$, $$|M(alpha) - N(beta)|_{mathcal{B}(ell^2(mathbb{N}))} = inf left {|M(alpha) - K |_{mathcal{B}(ell^2(mathbb{N}))} , : , K colon ell^2(mathbb{N}) to ell^2(mathbb{N}) textrm{ compact} right}.$$ Intimately connected with this result, it is then proven that the bidual of $mathcal{M}_0$ is isometrically isomorphic to $mathcal{M}$, $mathcal{M}_0^{ast ast} simeq mathcal{M}$. It follows that $mathcal{M}_0$ is an M-ideal in $mathcal{M}$. The dual space $mathcal{M}_0^ast$ is isometrically isomorphic to a projective tensor product with respect to Dirichlet convolution. The stated results are also valid for small Hankel operators on the Hardy space $H^2(mathbb{D}^d)$ of a finite polydisk.
Given a compact (Hausdorff) group $G$ and a closed subgroup $H$ of $G,$ in this paper we present symbolic criteria for pseudo-differential operators on compact homogeneous space $G/H$ characterizing the Schatten-von Neumann classes $S_r(L^2(G/H))$ fo
r all $0<r leq infty.$ We go on to provide a symbolic characterization for $r$-nuclear, $0< r leq 1,$ pseudo-differential operators on $L^{p}(G/H)$-space with applications to adjoint, product and trace formulae. The criteria here are given in terms of the concept of matrix-valued symbols defined on noncommutative analogue of phase space $G/H times widehat{G/H}.$ Finally, we present applications of aforementioned results in the context of heat kernels.
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 subspa
ce 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.
We investigate (uniform) mean ergodicity of (weighted) composition operators on the space of smooth functions and the space of distributions, respectively, both over an open subset of the real line. Among other things, we prove that a composition ope
rator with a real analytic diffeomorphic symbol is mean ergodic on the space of distributions if and only if it is periodic (with period 2). Our results are based on a characterization of mean ergodicity in terms of Ces`aro boundedness and a growth property of the orbits for operators on Montel spaces which is of independent interest.
Let $H$ be a compact subgroup of a locally compact group $G$ and let $m$ be the normalized $G$-invariant measure on homogeneous space $G/H$ associated with Weils formula. Let $varphi$ be a Young function satisfying $Delta_2$-condition. We introduce t
he notion of left module action of $L^1(G/H, m)$ on the Orlicz spaces $L^varphi(G/H, m).$ We also introduce a Banach left $L^1(G/H, m)$-submodule of $L^varphi(G/H, m).$
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
