On the linear extension complexity of regular n-gons

An exponential mean square stability for the invariant manifold [Formula: see text] of a nonlinear stochastic system is considered. The stability analysis is based on the [Formula: see text]-quadratic Lyapunov function technique. The local dynamics of the nonlinear system near manifold is described by the stochastic linear extension system. We propose a general notion of the projective stability (P-stability) and prove the following theorem. The smooth compact manifold [Formula: see text] is exponentially mean square stable if and only if the corresponding stochastic linear extension system is P-stable.

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A NON-EXTENDABLE BOUNDED LINEAR MAP BETWEEN C*-ALGEBRAS

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091599000978 ◽

2001 ◽

Vol 44 (2) ◽

pp. 241-248 ◽

Cited By ~ 1

Author(s):

Narutaka Ozawa

Keyword(s):

Linear Extension ◽

Subject Classification ◽

Primary 46L05 ◽

Bounded Linear ◽

Linear Map ◽

C Algebras ◽

Secondary 46L07

AbstractWe present an example of a $C^*$-subalgebra $A$ of $\mathbb{B}(H)$ and a bounded linear map from $A$ to $\mathbb{B}(K)$ which does not admit any bounded linear extension. This generalizes the result of Robertson and gives the answer to a problem raised by Pisier. Using the same idea, we compute the exactness constants of some Q-spaces. This solves a problem raised by Oikhberg. We also construct a Q-space which is not locally reflexive.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 46L07

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Linear extension sums as valuations on cones

Journal of Algebraic Combinatorics ◽

10.1007/s10801-011-0316-2 ◽

2011 ◽

Vol 35 (4) ◽

pp. 573-610 ◽

Cited By ~ 4

Author(s):

Adrien Boussicault ◽

Valentin Féray ◽

Alain Lascoux ◽

Victor Reiner

Keyword(s):

Linear Extension

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Type and Cotype Constants and the Linear Stability of Wigner’s Symmetry Theorem

Symmetry ◽

10.3390/sym11091107 ◽

2019 ◽

Vol 11 (9) ◽

pp. 1107

Author(s):

Javier Cuesta

Keyword(s):

Banach Spaces ◽

Linear Stability ◽

Linear Extension ◽

Transition Probabilities ◽

Linear Map ◽

Additive Error ◽

Type And Cotype

We study the relation between almost-symmetries and the geometry of Banach spaces. We show that any almost-linear extension of a transformation that preserves transition probabilities up to an additive error admits an approximation by a linear map, and the quality of the approximation depends on the type and cotype constants of the involved spaces.

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