Related papers: Generalized Kato Decomposition For Operator Matric…

Let ${\bf R}$ denote any of the following classes: upper (lower) semi-Fredholm operators, Fredholm operators, upper (lower) semi-Weyl operators, Weyl operators, upper (lower) semi-Browder operators, Browder operators. For a bounded linear…

A bounded linear operator $T$ on a Banach space $X$ is said to be generalized Drazin-meromorphic invertible if there exists a bounded linear operator $S$ acting on $X$ such that $TS=ST$, $STS=S$, $ TST-T$ is meromorphic. We shall say that…

We shall say that a bounded linear operator $T$ acting on a Banach space $X$ admits a generalized Kato-Riesz decomposition if there exists a pair of $T$-invariant closed subspaces $(M,N)$ such that $X=M\oplus N$, the reduction $T_M$ is Kato…

We introduce a new class which generalizes the class of B-Weyl operators. We say that $T\in L(X)$ is pseudo B-Weyl if $T=T_1\oplus T_2$ where $T_1$ is a Weyl operator and $T_2$ is a quasi-nilpotent operator. We show that the corresponding…

In \cite{koliha}, Koliha proved that $T\in L(X)$ ($X$ is a complex Banach space) is generalized Drazin invertible operator equivalent to there exists an operator $S$ commuting with $T$ such that $STS = S$ and $\sigma(T^{2}S -…

In this paper, we give some characterizations of the left and right generalized Drazin invertible bounded operators in Banach spaces by means of the single-valued extension property (SVEP). In particular, we show that a bounded operator is…

Let $S\in\mathcal{M}_d(\mathbb{C})^+$ be a positive semidefinite $d\times d$ complex matrix and let $\mathbf a=(a_i)_{i\in\mathbb{I}_k}\in \mathbb{R}_{>0}^k$, indexed by $\mathbb{I}_k=\{1,\ldots,k\}$, be a $k$-tuple of positive numbers. Let…

In this paper, we define and study the pseudo upper and lower semi B-Fredholm of bounded operators in a Banach space. In particular, we prove equality up to $S(T)$ between the left generalized Drazin spectrum and the pseudo upper semi…

The Kato's decomposition \cite[Theorem 4]{kato} is generalized to semi-B-Fredholm operators.

For the class of Hardy spaces and standard weighted Bergman spaces of the unit disk we prove that the spectrum of a generalized Ces\`aro operator $T_g$ is unchanged if the symbol $g$ is perturbed to $g+h$ by an analytic function $h$…

Let $X$ a Banach space and $T$ a bounded linear operator on $X.$ We denote by $S(T)$ the set of all $\lambda \in \cit$ such that $T$ does not have the single-valued extension property at $\lambda$. In this note we prove equality up to…

The generalized singular value decomposition (GSVD) of a matrix pair $\{A, L\}$ with $A\in\mathbb{R}^{m\times n}$ and $L\in\mathbb{R}^{p\times n}$ generalizes the singular value decomposition (SVD) of a single matrix. In this paper, we…

We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral…

In a right quaternionic Hilbert space, for a bounded right linear operator, the Kato S-spectrum is introduced and studied to a certain extent. In particular, it is shown that the Kato S-spectrum is a non-empty compact subset of the…

Generalized spectra of differential operators can be related to spectra of preconditioned discretized operators. Obtaining (estimates of) the eigenvalues of the preconditioned discretized operators may lead to better estimating of the…

Let \( H = (-\Delta)^m + V \) be a higher-order elliptic operator on \( L^2(\mathbb{R}^n) \), where \( V \) is a general bounded decaying potential. This paper focuses on the global Kato smoothing and Strichartz estimates for solutions to…

For $\beta>0$ and $p\ge 1$, the generalized Ces\`aro operator $$ \mathcal{C}_\beta f(t):=\frac{\beta}{t^\beta}\int_0^t (t-s)^{\beta-1}f(s)ds $$ and its companion operator $\mathcal{C}_\beta^*$ defined on Sobolev spaces…

Kato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely…

This paper derives the CS decomposition for orthogonal tensors (T-CSD) and the generalized singular value decomposition for two tensors (T-GSVD) via the T-product. The structures of the two decompositions are analyzed in detail and are…

We introduce the spaces $A^p_{\alpha, \beta}(\Omega)$ of $L^p$-solutions to the Vekua equation (generalized monogenic functions) $D w=\alpha\overline{w}+\beta w$ in a bounded domain in $\mathbb{R}^n$, where $D=\sum_{i=1}^n e_i \partial_i$…