Analogues for Hilbert C∗-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C∗-modules are studied with special attention paid on the differences with the well-known Hilbert space situation.

Jim Williams died in 1983. The surviving three authors are pleased to dedicate this paper to his memory. Abstract. Let C denote the category of Hilbert modules which are similar to con-tractive Hilbert modules. It is proved that if H 0 ; H 2 C and if H 1 is similar to an isometric Hilbert module, then the sequence 0 ! H 0 ! H ! H 1 ! 0 splits. Thus the isometric Hilbert modules are projective i...

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal unit is a simple generator embeds (weakly) monoidally into the category of pre-Hilbert spaces and adjointable maps, preserving adjoint morphisms and all fini...

in this paper we proved that every g-riesz basis for hilbert space $h$ with respect to $k$ by adding a condition is a riesz basis for hilbert $b(k)$-module $b(h,k)$. this is an extension of [a. askarizadeh,m. a. dehghan, {em g-frames as special frames}, turk. j. math., 35, (2011) 1-11]. also, we derived similar results for g-orthonormal and orthogonal bases. some relationships between dual fram...

The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown whether toric Hilbert schemes are connected. We construct a graph on all the monomial ideals on the scheme, called the flip graph, and prove that the toric Hilbert scheme is connected if and only if the flip graph is ...

Hilbert geometry is a metric geometry that extends the hyperbolic Cayley-Klein geometry. In this video, we explain the shape of balls and their properties in a convex polygonal Hilbert geometry. First, we study the combinatorial properties of Hilbert balls, showing that the shapes of Hilbert polygonal balls depend both on the center location and on the complexity of the Hilbert domain but not o...

The Gravitational, Electromagnetic, Weak & the Strong force are here brought together under a single roof via an extension of Reimann geometry to a new geometry (coined Reimann-Hilbert Space); that unlike Reimann geometry, preserves both the length and the angle of a vector under parallel transport. The affine connection of this new geometry – the Reimann-Hilbert Space, is a tensor and this lea...

This paper concerns a rather concrete phenomenon in abstract operator algebras. The main examples of the algebras we study are algebras of singular integral operators (pseudo-differential operators of order zero). As everyone knows, the Fredhohn index of a pseudo-differential operator depends only on its symbol and the Atiyah-Singer Index Theorem gives an explicit formula for computing the depe...

Emotion feature extraction is the key to speech emotional recognition. And ensemble empirical mode decomposition(EEMD) is a newly developed method aimed at eliminating emotion mode mixing present in the original empirical mode decomposition(EMD). To evaluate the performance of this new method, this paper investigates the effect of a parameters pertinent to EEMD: speech emotional envelope. First...

Following the “decomposition-and-ensemble” principle, the empirical mode decomposition (EMD)-based modeling framework has been widely used as a promising alternative for nonlinear and nonstationary time series modeling and prediction. The end effect, which occurs during the sifting process of EMD and is apt to distort the decomposed sub-series and hurt the modeling process followed, however, ha...