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28 March 2024
 
  » arxiv » math.FA/0211359

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Total Dilations
Jean-Christophe Bourin ;
Date 22 Nov 2002
Subject Functional Analysis MSC-class: 47A20 | math.FA
Abstract(1) Let $A$ be an operator on a space ${cal H}$ of even finite dimension. Then for some decomposition ${cal H}={cal F}oplus{cal F}^{perp}$, the compressions of $A$ onto ${cal F}$ and ${cal F}^{perp}$ are unitarily equivalent. (2) Let ${A_j}_{j=0}^n$ be a family of strictly positive operators on a space ${cal H}$. Then, for some integer $k$, we can dilate each $A_j$ into a positive operator $B_j$ on $oplus^k{cal H}$ in such a way that: (i) The operator diagonal of $B_j$ consists of a repetition of $A_j$. (ii) There exist a positive operator $B$ on $oplus^k{cal H}$ and an increasing function $f_j : (0,infty)longrightarrow(0,infty)$ such that $B_j=f_j(B)$.
Source arXiv, math.FA/0211359
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