We characterise imaginaries (up to interdefinability) in Hilbert spaces using a Galois theory for compact unitary groups.

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

The basic mathematical framework for super Hilbert spaces over a Graßmann algebra with a Graßmann number-valued inner product is formulated. Super Hilbert spaces over infinitely generated Graßmann algebras arise in the functional Schrödinger representation of spinor quantum field theory in a natural way. a email: [email protected]

This paper is concerned with the problem of finding a lower bound for certain matrix operators such as Hausdorff and Hilbert matrices on sequence spaces lp(w) and Lorentz sequence spaces d(w,p), which is recently considered in [7,8], similar to [13] considered by J. Pecaric, I. Peric and R. Roki. Also, this study is an extension of some works which are studied before in [1,2,7,8].

In this paper we consider a number of sequence and function spaces that are known to be homeomorphic to the countable product of the linear space σ. The spaces we are interested in have a canonical imbedding in both a topological Hilbert space and a Hilbert cube. It turns out that when we consider these spaces as subsets of a Hilbert cube then there is only one topological type. For imbeddings ...

in this paper we propose a relatively new semi-analytical technique to approximate the solution ofnonlinear multi-order fractional differential equations (fdes). we present some results concerning to the uniqueness of solution of nonlinear multi-order fdes and discuss the existence of solution for nonlinear multi-order fdes in reproducing kernel hilbert space (rkhs). we further give an error an...

My research concerns the study of the symmetries and the geometry of the basic Hilbert spaces that appear in harmonic analysis and applied mathematics, i.e., the Hilbert spaces of functions (or more generally sections of certain vector bundels) on geometric spaces. For example when I study the Hilbert spaces of functions on vector spaces of the form F where F is a …eld –which can be either a …n...

That is, maps from A to B∗ are given by integral kernels in (A⊗B)∗. However, the validity of this adjunction depends on existence of a genuine tensor product. We recall in an appendix the demonstration that infinitedimensional Hilbert spaces do not have tensor products. Also, we must specify the topology on the duals B∗ and (A⊗B)∗. The strongest conclusion gives these the strong topology, as co...

That is, maps from A to B∗ are given by integral kernels in (A⊗B)∗. However, the validity of this adjunction depends on existence of a genuine tensor product. We recall in an appendix the demonstration that infinitedimensional Hilbert spaces do not have tensor products. Also, we must specify the topology on the duals B∗ and (A⊗B)∗. The strongest conclusion gives these the strong topology, as co...