Projections libérantes

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A note on lifting projections

Suppose $pi:mathcal{A}rightarrow mathcal{B}$ is a surjective unital $ast$-homomorphism between C*-algebras $mathcal{A}$ and $mathcal{B}$, and $0leq aleq1$ with $ain  mathcal{A}$. We give a sufficient condition that ensures there is a proection $pin mathcal{A}$ such that $pi left( pright) =pi left( aright) $. An easy consequence is a result of [L. G. Brown and G. k. Pedersen, C*-algebras of real...

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Ideal Projections and forcing Projections

It is well known that saturation of ideals is closely related to the “antichain-catching” phenomenon from Foreman-Magidor-Shelah [10]. We consider several antichain-catching properties that are weaker than saturation, and prove: (1) If I is a normal ideal on ω2 which satisfies stationary antichain catching, then there is an inner model with a Woodin cardinal; (2) For any n ∈ ω, it is consistent...

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a note on lifting projections

suppose $pi:mathcal{a}rightarrow mathcal{b}$ is a surjective unital $ast$-homomorphism between c*-algebras $mathcal{a}$ and $mathcal{b}$, and $0leq aleq1$ with $ain  mathcal{a}$. we give a sufficient condition that ensures there is a proection $pin mathcal{a}$ such that $pi left( pright) =pi left( aright) $. an easy consequence is a result of [l. g. brown and g. k. pedersen, c*-algebras of real...

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Random Projections

We consider the distribution of matrices R such that each R(i, j) is drawn independently from a normal distribution with mean zero and variance 1, R(i, j) ∼ N (0, 1). We show that for this distribution Equation 1 holds for some k ∈ O(log(n)/ε). First consider the random variable z = ∑d i=1 r(i)x(i) where r(i) ∼ N (0, 1). To understand how the variable z distributes we recall the two-stability o...

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Predictive Projections

This paper addresses the problem of learning control policies in very high dimensional state spaces. We propose a linear dimensionality reduction algorithm that discovers predictive projections: projections in which accurate predictions of future states can be made using simple nearest neighbor style learning. The goal of this work is to extend the reach of existing reinforcement learning algor...

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ژورنال

عنوان ژورنال: Études françaises

سال: 1972

ISSN: 0014-2085,1492-1405

DOI: 10.7202/036521ar