Related papers: Growth conditions and inverse producing extensions
Several characterizations of EP and normal Moore-Penrose invertible Banach algebra elements will be considered. The Banach space operator case will be also studied. The results of the present article will extend well known facts obtained in…
Let $(G,d)$ be a metric space with the counting measure $\mu$ satisfying some growth conditions. Let $\omega(x,y)=(1+d(x,y))^\delta$ for some $0<\delta\leq1$. Let $0<p\leq1$. Let $\mathcal A_{p\omega}$ be the collection of kernels $K$ on…
We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…
We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…
Let $T$ be a positive operator on a complex Banach lattice. It is a long open problem whether the peripheral spectrum $\sigma_{\operatorname{per}}(T)$ of $T$ is always cyclic. We consider several growth conditions on $T$, involving its…
Let $A$ be an unbounded operator on a Banach space $X$. It is sometimes useful to improve the operator $A$ by extending it to an operator $B$ on a larger Banach space $Y$ with smaller spectrum. It would be preferable to do this with some…
It is proved that a commutative algebra $A$ of operators on a reflexive real Banach space has an invariant subspace if each operator $T\in A$ satisfies the condition $$\|1- \varepsilon T^2\|_e \le 1 + o(\varepsilon) \text{ when }…
It is proved that a commutative algebra $A$ of operators in a reflexive real Banach space has an invariant subspace if each operator $T\in A$ satisfies the condition $$\|1- \varepsilon T^2\|_e \le 1 + o(\varepsilon) \text{ when }…
The Roper--Suffridge extension operator and its modifications are powerful tools to construct biholomorphic mappings with special geometric properties. The first purpose of this paper is to analyze common properties of different extension…
Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (\alpha_j -A)^{-1}$ are given. Several examples are considered.
Arbitrary operator A on a Banach space X which is the generator of C_0-group with certain growth condition at infinity is considered. The relationship between its exponential type entire vectors and its spectral subspaces is found. Inverse…
An algebra of bounded linear operators on a Banach space is said to be {\em strongly compact} if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be {\em strongly…
We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…
The main concern of this note is the Moore-Penrose inverse in the context of Banach spaces and algebras. Especially attention will be given to a particular class of elements with the aforementioned inverse, namely EP Banach space operators…
The paper deals with extension of bounded bilinear maps$.$ It gives a necessary and sufficient condition for extending a bounded bilinear map on the Cartesian product of subspaces of Banach spaces$.$ This leads to a full characterization…
In this article properties of the $(b, c)$-inverse, the inverse along an element, the outer inverse with prescribed range and null space $A^{(2)}_{T, S}$ and the Moore-Penrose inverse will be studied in the contexts of Banach spaces…
By strengthening one of the hypotheses of a well-known sufficient condition for the hypercyclicity of linear operators in Banach spaces, we arrive at a sufficient condition for linear chaos and reveal consequences of the latter for…
We study an abstract linear operator equation on a Banach space by using the inverse of the sum of two sectorial operators. We prove that the boundedness of a special type of operator valued $H^\infty$-calculus is sufficient for maximal…
Let $T$ be a quasinilpotent operator on a Banach space. Under assumptions of a certain nonsymmetry in the growth of the resolvent of $T$, it is proved that every operator in the commutant of $T$ is not unicellular. In particular, $T$ has…
In this paper, we present new necessary and sufficient conditions under which the sum of two group invertible elements in a Banach algebra has group inverse. We then apply these results to block operator matrices over Banach spaces. The…