Linearly isometric
Nettet10.4. The Unitary Group, Unitary Matrices 299 Remarks: (i) In the Euclidean case, we proved that the assumption f(v)−f(u) = v −u for all u,v ∈ E and f(0) = 0 (2 ) implies … NettetA classical Banach space is a Banach space X whose dual space is linearly isometric to Lp (j1, IR) (or Lp (j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ …
Linearly isometric
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NettetIn this paper, we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C (Ω). We obtain that if the set sm. S 1 ( E) of all … Nettet1. nov. 2024 · We present a short proof for the fact that if smooth real Banach spaces of dimension three or higher have isomorphic Birkhoff–James orthogonality structures, then they are (linearly) isometric to each other. This generalizes results of …
NettetIn the area of mathematics known as functional analysis, a reflexive space is a locally convex topological vector space (TVS) for which the canonical evaluation map from into … NettetProof of Theorem A. Since В is linearly isometric to a C*-algebra and every product on a C*-algebra is Arens regular ([26], [33]), it follows that the product of B** (equal to the third Arens transpose of that of B) is w*-continuous in each of its variables. Then, since В has an approximate unit bounded by one, a
NettetThe structure theorems concern necessary and sufficient conditions that a general Banach space is linearly isometric to a classical Banach space. They are framed in terms of conditions on the norm of the space X, conditions on the dual space X*, and on (finite dimensional) subspaces of X. Nettet23. nov. 2016 · Is there a Banach space $Z$ such that $X$ is lineraly isometric to the dual of $Z$: $X=Z^*$. I think that the answer is no, but I do not have a counterexample. Since $L_1$ is not isometric to any dual Banach space, maybe one can find a dual Banach space which is isomorphic to $L_1$...
NettetThe operator T is called an isometric quotient mapping provided Tq is an isometry, which is the case if and only if T∗ is an isometric embedding. If S: X → Z is an isomorphic embedding, then S∗ is an isometric quotient mapping if and only if S is an isometric embedding. All notation and terminology, not otherwise explained, are as in [LT].
Nettet15. jan. 2010 · In this paper, we show that if V 0 is a 1-Lipschitz mapping between unit spheres of two AL p -spaces with p > 2 and −V 0(S 1(L p )) ⊂ V 0(S 1(L p )), then V 0 … solano historyNettet17. jun. 2024 · Abstract. Cheeger–Gromoll’s classical splitting theorem asserts that, if a complete Riemannian manifold of nonnegative Ricci curvature includes a straight line (an isometric copy of the real line), then it isometrically splits off the real line. This beautiful theorem and its generalizations have had quite rich applications in the structure ... slumber clubNettet1. jan. 2014 · 5 On Linearly Isometric Extensions for Nonexpansive Mappings Between Unit Spheres G. Ding [ 10 ] first discussed the isometric extension problem between Hilbert spaces without the assumption of the surjectivity, and he showed that a 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real … slumber coachNettet15. jan. 2010 · In this paper, we show that if V 0 is a 1-Lipschitz mapping between unit spheres of two AL p -spaces with p > 2 and −V 0(S 1(L p )) ⊂ V 0(S 1(L p )), then V 0 can be extended to a linear isometry defined on the whole space. If 1 < p < 2 and V 0 is an “anti-1-Lipschitz” mapping, then V 0 can also be linearly and isometrically extended. slumber cloud stratus sheet setNettetElements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. slumber cloud stratus cooling sheet setNettetThe space C (2 N ) is linearly isomorphic(but not isometric) to C ([0 , C (2 N ) ⊕ C (2 N ) with the maximum norm is linearly isometric to C (2 N ), because thedisjoint sum of two copies of the Cantor set is homeomorphic to the Cantor set.Thus, Example 1.2 provides a left-universal operator on C (2 N ).Another, not so well known, universal ... slumbercloud silk pillowcaseNettet1 Answer. This is true for real vector spaces by the Mazur-Ulam theorem which states that a surjective distance-preserving linear map of one real normed space onto another is … slumber cloud mattress cover