let  be a hilbert space of functions analytic on a plane domain  such that for every  in  the functional of evaluation at  is bounded. assume further that  contains the constants and admits multiplication by the independent variable , , as a bounded operator. we give sufficient conditions for  to be reflexive for all positive integers .

in this note, we characterize chebyshev subalgebras of unital jb-algebras. we exhibit that if b is chebyshev subalgebra of a unital jb-algebra a, then either b is a trivial subalgebra of a or a= h r .l, where h is a hilbert space

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrödinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave f...

The ability of the Rigged Hilbert Space formalism to deal with continuous spectrum is demonstrated within the example of the square barrier potential. The non-square integrable solutions of the time-independent Schrödinger equation are used to define Dirac kets, which are (generalized) eigenvectors of the Hamiltonian. These Dirac kets are antilinear functionals over the space of physical wave f...

the aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von neumann algebra on a hilbert space with a normal faithful semi-finite trace $tau$. the submajorization inequalities generalize some results due to zhang, furuichi and lin, etc..

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. This is in sharp contrast to the behavior of operators on `2, and so rigid spaces are, from the viewpoint of functional analysis, fundamentally different from Hilbert space. Nevertheless, we show in this paper that a rigid space can be constructed which is topologically homeomorp...