Contractive Projections in $C_p$American Mathematical Soc., 1992 - 109 עמודים This work is devoted to the study of contractive projection (that is, norm-one idempotent operators) on Cp where Cp denotes the von Meumann-Schatten p-classes. The authors show that the range of a contractive projection on Cp(Pi1?, p=2) is the direct sum of Cp-ideals of classical Cartan factors. |
תוכן
| 1 | |
1 Properties of contractive projections on Csubp which depend on smoothness strict convexity and refiexivity | 7 |
2 JCtriples and the formulation of the main result | 12 |
3 Differentiation formulas and Schur multipliers | 24 |
4 Connection between a contractive projection and Peirce projections associated with elements in its range | 37 |
5 Existence of atoms | 43 |
6 Basic relations between atoms | 51 |
7 Structure of Nconvex subspaces of Csubp | 61 |
8 Conclusion of the proof of the Main Theorem and applications | 80 |
9 Families of contractive projections and concluding remarks | 92 |
References | 104 |
מהדורות אחרות - הצג הכל
Contractive Projections in Cp, מהדורה 459 <span dir=ltr>Jonathan Arazy</span>,<span dir=ltr>Yaakov Friedman</span> אין תצוגה מקדימה זמינה - 1992 |
מונחים וביטויים נפוצים
a₁ algebra assume atom of X₁(x Banach space bicontractive bounded C₁ classical Cartan factor closed subspace cog-grid colinear colinear family completes the proof conjugate-linear contractive projection Cp-ideals defined denote Department of Mathematics differentiable direct sum exist orthogonal fact finite follows Hilbert space implies indecomposable indecomposable subspaces indecomposable summands JB*-triple linear span linear subspace Main Theorem Math module monomorphism monotone basis Moreover morphism non-zero normalized elements Np(x Np(Y operator norm orthogonal elements orthonormal P₁ partial isometries Peirce decomposition polar decomposition projection from Cp projection on Cp proof of Lemma proof of Theorem Proposition 2.2 prove ranges of contractive rank respect satisfies condition Schmidt series Schur multipliers Section self-adjoint span spectral family subspace of Cp tensor product representation Theorem 2.4 theory triple isometries triple monomorphism triple product Vp(µ Wp(v X₁ Xi,j y₁ Z₁ Zorn's lemma