we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

We establish the following Hilbert-space analogue of Gleason-Kahane-\.Zelazko theorem. If $\mathcal{H}$ is a reproducing kernel Hilbert space with normalized complete Pick kernel, and if $\Lambda$ linear functional on such that $\Lambda(1)=1$ $\Lambda(f)\ne0$ for all cyclic functions $f\in\mathcal{H}$, then multiplicative, in sense $\Lambda(fg)=\Lambda(f)\Lambda(g)$ $f,g\in\mathcal{H}$ $fg\in\m...

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

For spaces of analytic functions defined on an open set in $\mathbb{C}^n$ that satisfy certain nice properties, we show operators preserve shift-cyclic are necessarily weighted composition operators. Examples for which this result holds true consist the Hardy space $H^p(\mathbb{D}^n) \, (0 < p \infty)$, Drury-Arveson $\mathcal{H}^2_n$, and Dirichlet-type $\mathcal{D}_{\alpha} (\alpha \in \mathb...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.