GEOMETRY OF THE LEFT ACTION OF THE P-SCHATTEN GROUPS

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IORIO Y LUCERO MARIA EUGENIA DI

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

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Paper Information

Journal: BANACH JOURNAL OF MATHEMATICAL ANALYSIS Year:2013 | Volume:7 | Issue:1 Page(s): 73-87

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Title

GEOMETRY OF THE LEFT ACTION OF THE P-SCHATTEN GROUPS

Author(s)

IORIO Y LUCERO MARIA EUGENIA DI | Issue Writer Certificate

Keywords

ANALYTIC SUBMANIFOLD

FINSLER METRIC

RIEMANNIAN METRIC

SCHATTEN OPERATOR

Abstract

Let H be an infinite dimensional Hilbert space, Bp (H) the p-Schatten class of H and Up (H) be the Banach-Lie group of unitary operators which are p-Schatten perturbations of the identity. Let A be a bounded self-adjoint operator in H. We show thatOA:={UA:UÎUp(H)}is a smooth submanifold of the affine space A+Bp (H) if only if A has closed range. Furthermore, it is a homogeneous reductive space of Up (H). We intro- duce two metrics: one via the ambient FINSLER METRIC induced as a submanifold of A+Bp (H), the other, by means of the quotient FINSLER METRIC provided by the homogeneous space structure. We show that OA is a complete metric space with the recti able distance of these metrics.

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APA: Copy

IORIO Y LUCERO, MARIA EUGENIA DI. (2013). GEOMETRY OF THE LEFT ACTION OF THE P-SCHATTEN GROUPS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 7(1), 73-87. SID. https://sid.ir/paper/317028/en

Vancouver: Copy

IORIO Y LUCERO MARIA EUGENIA DI. GEOMETRY OF THE LEFT ACTION OF THE P-SCHATTEN GROUPS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS[Internet]. 2013;7(1):73-87. Available from: https://sid.ir/paper/317028/en

IEEE: Copy

MARIA EUGENIA DI IORIO Y LUCERO, “GEOMETRY OF THE LEFT ACTION OF THE P-SCHATTEN GROUPS,” BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol. 7, no. 1, pp. 73–87, 2013, [Online]. Available: https://sid.ir/paper/317028/en

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