منابع مشابه
Isometries and the Linear Algebra of Quadratic
0.1. 2D. In the context of linear algebra a plane is a two-dimensional real vector space. A basis for a plane consists of any two vectors E1,E2 which span the plane. ‘Spanning’ means that any vector v⃗ in the plane can be written as v⃗ = uE1 + vE2 with u, v ∈ R. It is a theorem that for two vectors in the plane “spanning” is equivalent to being “linearly independent”. The ‘linearly independent pa...
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and Applied Analysis 3 Now we recall definitions and some properties of the Smirnov class, the Privalov class, the Bergman-Privalov class, and the Zygmund F-algebra on Bn or D. The space of all holomorphic functions on X Bn or D is denoted by H X . For each 0 < p ≤ ∞, the Hardy space is denoted by H X with the norm ‖ · ‖p. 2.1. Smirnov Class N∗ X Let X ∈ {Bn, Dn}. The Nevanlinna class N X on X ...
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Given two complex Hilbert spaces H and K, let S(B(H)) and S(B(K)) denote the unit spheres of the C∗-algebras B(H) and B(K) of all bounded linear operators on H and K, respectively. We prove that every surjective isometry f : S(B(K)) → S(B(H)) admits an extension to a surjective complex linear or conjugate linear isometry T : B(K) → B(H). This provides a positive answer to Tingley’s problem in t...
متن کاملf-Orthomorphisms and f-Linear Operators on the Order Dual of an f-Algebra
and Applied Analysis 3 It should be noted that the mapping V : A∼ n → Orth A∼ defined by V F VF for all F ∈ A∼ n, where VF f F · f for every f ∈ A∼, is an algebra and Riesz isomorphism cf. 2, Proposition 2.2 . Theorem 2.1. For 0 ≤ f ∈ A∼, Tf is an interval preserving lattice homomorphism. Proof. Clearly, Tf is linear and positive. Since the mapping V is a lattice homomorphism and VF, VG ∈ Orth ...
متن کاملIsometries and Approximate Isometries
Some properties of isometric mappings as well as approximate isometries are studied. 2000 Mathematics Subject Classification. Primary 46B04. 1. Isometry and linearity. Mazur and Ulam [17] proved the following well-known result concerning isometries, that is, transformations which preserve distances. Theorem 1.1. Given two real normed vector spaces X and Y , let U be a surjective mapping from X ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-11146-8