It is known, by Gelfand theory, that every commutative JB∗-triple admits a representation as space of continuous functions the form C0T(L)={a∈C0(L):a(λt)=λa(t),∀λ∈T,t∈L},where L principal T-bundle and T denotes unit circle in C. We provide full technical description all orthogonality preserving (non-necessarily nor bijective) linear maps between JB∗-triples. Among consequences this representati...

A C-linear map θ (not necessarily bounded) between two Hilbert C-modules is said to be ‘orthogonality preserving’ if 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We prove that if θ is an orthogonality preserving map from a full Hilbert C0()-module E into another Hilbert C0()-module F that satisfies a weaker notion of C0()-linearity (called ‘localness’), then θ is bounded and there exists φ ∈ Cb()+...

At EUROCRYPT 2012 Pandey and Rouselakis introduced the notion of property preserving symmetric encryption which enables checking for a property on plaintexts by running a public test on the corresponding ciphertexts. Their primary contributions are: (i) a separation between ‘find-then-guess’ and ‘left-or-right’ security notions; (ii) a concrete construction for left-or-right secure orthogonalit...

SUMMARY Recently the GMRESR inner-outer iteration scheme for the solution of linear systems of equations has been proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski 1] and Saad (FGMRES) 10]. The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a ne...

We study the norm derivatives in context of Birkhoff–James orthogonality real Banach spaces. As an application this, we obtain a complete characterization left-symmetric points and right-symmetric space terms derivatives. strong $$\ell _1^n$$ _\infty ^n$$ also relation defined by some newly introduced variation orthogonality. further orthogonality, approximate smoothness attainment bounded bili...

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 dene the concepts of bessel, hilbert ov-basis and obt...

Two distinct projections of finite rank m are adjacent if their difference is an operator two or, equivalently, the intersection images (m−1)-dimensional. We extend this adjacency relation on other conjugacy classes finite-rank self-adjoint operators which leads to a natural generalization Grassmann graphs. Let C be class formed by with eigenspaces dimension greater than 1. Under assumption tha...