Related papers: Local commutants and ultrainvariant subspaces

We investigate if, for a locally compact group $G$, the Fourier algebra $A(G)$ is biflat in the sense of quantized Banach homology. A central role in our investigation is played by the notion of an approximate indicator of a closed subgroup…

Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\mathfrak{H}_0$ is of codimension 1, we…

It is established that every derivation continuous with respect to the local measure topology acting on the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a von Neumann algebra $\mathcal{M}$ is necessary…

It is well known that the structure of nontrival invariant subspaces for the shift operator on the Bergman space is extremely complicated and very little is known about their specific structures, and that a complete description of the…

In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with…

We consider the Fr\'echet ${}^*$-algebra $L(s',s)$ of the so-called smooth operators, i.e. continuous linear operators from the dual $s'$ of the space $s$ of rapidly decreasing sequences into $s$. This algebra is a non-commutative analogue…

We define the notion of strong spectral invariance for a dense Frechet subalgebra A of a Banach algebra B. We show that if A is strongly spectral invariant in a C*-algebra B, and G is a compactly generated polynomial growth Type R Lie…

Consider a bounded strongly pseudo-convex domain $\Omega $ with a smooth boundary in $\mathbb{C}^n$. Let $\mathcal{T}$ be the Toeplitz algebra on the Bergman space $L^2_a(\Omega )$. That is, $\mathcal{T}$ is the $C^\ast $-algebra generated…

Let $E$ be a Banach space that does not contain any copy of $\ell^1$ and $\A$ be a non commutative $C^*$-algebra. We prove that every absolutely summing operator from $\A$ into $E^*$ is compact, thus answering a question of Pe\l czynski. As…

It is well known that in the commutative case, i.e. for $A=C(X)$ being a commutative C*-algebra, compact selfadjoint operators acting on the Hilbert C*-module $H_A$ (= continuous families of such operators $K(x)$, $x\in X$) can be…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

Let $\mathcal{H}$ be an infinite dimensional real or complex separable Hilbert space. We introduce a special type of a bounded linear operator $T$ and its important relation with invariant subspace problem on $\mathcal{H}$: operator $T$ is…

We consider the shift operator $M_z$, defined on the Bloch space and the little Bloch space and we study the corresponding lattice of invariant subspaces. The index of a closed invariant subspace $E$ is defined as $\text{ind}(E) =…

An operator $T$ acting on a Banach space $X$ is said to be super-recurrent if for each open subset $U$ of $X$, there exist $\lambda\in\mathbb{K}$ and $n\in \mathbb{N}$ such that $\lambda T^n(U)\cap U\neq\emptyset$. In this paper, we…

Given an n-tuple of multiplication operators on the Bergman space of a bounded pseudoconvex domain in C^n, we study the algebra of their commutants. In particular, we give a geometric description of the maximal C*-subalgebra of this…

Let $T:D(T)\rightarrow H_2$ be a densely defined closed operator with domain $D(T)\subset H_1$. We say $T$ to be absolutely minimum attaining if for every closed subspace $M$ of $H_1$, the restriction operator $T|_M:D(T)\cap M\rightarrow…

We study the spectrum of operators $aT\in B(H)$ on a Hilbert space $H$ where $T$ is an isometry and $a$ belongs to a commutative $C^*$-subalgebra $C(X)\cong A\subseteq B(H)$ such that the formula $L(a)=T^*aT$ defines a faithful transfer…

This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…

In this article, we characterize the Beurling and Model subspaces of the Hardy-Hilbert space $H^2(\mathbb{D})$ invariant under the composition operator $C_{\phi_a}f=f\circ\phi_a$, where $\phi_a(z) = az + 1 - a$ for $a \in (0,1)$ is an…

For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present…