Related papers: On the norm closure problem for complex symmetric …
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of complex-valued harmonic functions exhibit many properties…
For every fixed $\epsilon$ $\in$ (0, 1), we construct an operator on the separable Hilbert space which is $\delta$-hypercyclic for all $\delta$ $\in$ ($\epsilon$, 1) and which is not $\delta$-hypercyclic for all $\delta$ $\in$ (0,…
Several refinements of norm and numerical radius inequalities of bounded linear operators on a complex Hilbert space are given. In particular, we show that if $A$ is a bounded linear operator on a complex Hilbert space, then $$…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
In this paper, we establish results about operators similar to their adjoints. This is carried out in the setting of bounded and also unbounded operators on a Hilbert space. Among the results, we prove that an unbounded closed operator…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
This note deals with a problem of the probabilistic Ramsey theory in functional analysis. Given a linear operator $T$ on a Hilbert space with an orthogonal basis, we define the isomorphic structure $\Sigma(T)$ as the family of all subsets…
This note deals with the operator $T^*T$, where $T$ is a densely defined operator on a complex Hilbert space. We reprove a recent result of Z. Sebesty\'en and Zs. Tarcsay [13]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed. In…
Let $X,Y$ be normal bounded operators on a Hilbert space such that $e^X=e^Y$. If the spectra of $X$ and $Y$ are contained in the strip $\s$ of the complex plane defined by $|\Im(z)|\leq \pi$, we show that $|X|=|Y|$. If $Y$ is only assumed…
In this paper we prove that Dirac operators on non-compact complete orbifolds which are sufficiently regular at infinity, admit a unique extension. Additonally, we prove a generalized orbifold Stokes'/Divergence theorem.
In this paper, we investigate when weighted composition operators acting on Dirichlet spaces $\mathcal{D}(\mathbb{B}_{N})$ are complex symmetric with respect to some special conjugations, and provide some characterizations of Hermitian…
A sequence of operators $T_n$ from a Hilbert space ${\mathfrak H}$ to Hilbert spaces ${\mathfrak K}_n$ which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator $T$ from…
We shall prove that the Hilbert cube cannot be separated by a weakly infinite dimensional subset. As a corollary we obtain that the complement of a weakly infinite dimensional subset of the space of complete non negatively curved metrics is…
It is shown that if the C operator for a PT-symmetric Hamiltonian with simple eigenvalues is not unique, then it is unbounded. Apart from the special cases of finite-matrix Hamiltonians and Hamiltonians generated by differential expressions…
We prove that every continuous function on a separable infinite-dimensional Hilbert space X can be uniformly approximated by smooth functions with no critical points. This kind of result can be regarded as a sort of very strong approximate…
We completely characterize the Crawford number attainment set and the numerical radius attainment set of a bounded linear operator on a Hilbert space. We study the intersection properties of the corresponding attainment sets of numerical…
We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…
We consider the unitary group $\U$ of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever $\U$ acts by isometries on a metric space, every orbit is bounded. Equivalently, $\U$ is not the…
The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…
We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it "operator ball") has a restricted form of normal structure if we endow it with a hyperbolic metric…