Related papers: Perturbed Operators on Banach Spaces

Global folds between Banach spaces are obtained from a simple geometric construction: a Fredholm operator $T$ of index zero with one dimensional kernel is perturbed by a compatible nonlinear term $P$. The scheme encapsulates most of the…

In an earlier paper, we showed that the moduli space of deformations of a smooth, compact, orientable special Lagrangian submanifold L in a symplectic manifold X with a non-integrable almost complex structure is a smooth manifold of…

We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Short-Time Fourier Transform for functions, in particular…

Let ${\mathcal B}(H)$ denote the Banach algebra of all bounded linear operators on a complex Hilbert space $H$ with $\dim H\geq 3$, and let $\mathcal A$ and $\mathcal B$ be subsets of ${\mathcal B}(H)$ which contain all rank one operators.…

We prove that if X is an infinite-dimensional Banach space with C^p smooth partitions of unity, then X and X\K are C^p diffeomorphic, for every weakly compact subset K of X.

$C^1$ linearization is of special significance because it preserves smooth dynamical behaviors and distinguishes qualitative properties in characteristic directions. However, $C^1$ smoothness is not enough to guarantee $C^1$ linearization.…

In this article we study cohomology of a group with coefficients in representations on Banach spaces and its stability under deformations. We show that small, metric deformations of the representation preserve vanishing of cohomology. As…

We characterize the limited operators by differentiability of convex continuous functions. Given Banach spaces $Y$ and $X$ and a linear continuous operator $T: Y \longrightarrow X$, we prove that $T$ is a limited operator if and only if,…

We prove necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. These conditions are formulated in terms of indices of submultiplicative functions…

Following the definition of perturbed metric space, in this paper, some fixed point theorems are established for $ F $-perturbed mappings in complete perturbed metric spaces and justify the result by counter example. Finally, an application…

In this paper, we investigate the invertibility of $I_Y+\delta TT^+$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^+$ and $\delta T$ is a linear operator whose domain contains $D(T)$ and range is contained in…

We prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of…

In this paper we study some basic properties of bicomplex linear operators on bicomplex Hilbert spaces. Further we discuss some applications of Hahn-Banach theorem on bicomplex Banach modules. We also introduce and discuss some bicomplex…

Our main result concerns the following condition: {\bf Condition C.} Let $X$ be a Banach space. A $C^1$ function $f:X\rightarrow \mathbb{R}$ satisfies Condition C if whenever $\{x_n\}$ weakly converges to $x$ and $\lim…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

In this paper we study operators originated from semi-B-Fredholm theory and as a consequence we get some results regarding boundaries and connected hulls of the corresponding spectra. In particular, we prove that a bounded linear operator…

In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…

For an operator $A$ on a complex Banach space $X$ and a closed subspace $M\subseteq X$, the local commutant of $A$ at $M$ is the set $C(A;M)$ of all operators $T$ on $X$ such that $TAx=ATx$ for every $x\in M$. It is clear that $ C(A;M)$ is…

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…

We prove that if $0<\a<1$ and $f$ is in the H\"older class $\L_\a(\R)$, then for arbitrary self-adjoint operators $A$ and $B$ with bounded $A-B$, the operator $f(A)-f(B)$ is bounded and $\|f(A)-f(B)\|\le\const\|A-B\|^\a$. We prove a similar…