منابع مشابه
Orthogonality preserving mappings on inner product C* -modules
Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...
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In this paper, we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$. We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator. Also, we prove that every compact normal operator is a strongly orthogo...
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1. Introduction. The investigation leading to this publication was motivated by a desire to try to understand the structure of a linear unital mapping ϕ from a unital algebra A of matrices contained in M h (C) into M n (C) which has the property that an invertible element in A is mapped into an invertible in M n (C). The interest in this question was raised by some earlier results on a linear i...
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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...
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A mapping f : M → N between Hilbert C∗-modules approximately preserves the inner product if ‖〈f(x), f(y)〉 − 〈x, y〉‖ ≤ φ(x, y), for an appropriate control function φ(x, y) and all x, y ∈ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert C∗modules on more general restricted domains. In particular, we investigate some asympt...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.07.062