A Brief Introduction to Berezin–Toeplitz Operators on Compact Kähler Manifolds by Yohann Le Floch

Author:Yohann Le Floch
Language: eng
Format: epub
ISBN: 9783319946825
Publisher: Springer International Publishing

This yields that is injective, where .

Exercise 4.5.3.

Prove the last claim above. Hint: Start by showing that there exists such that .

Proof of Proposition 4.5.1. We may, and will, assume without loss of generality that . Let

be the map sending to , extended by linearity; is clearly injective. Now, let be as in the previous lemma. Since is an injective linear map between two spaces of the same dimension, it is surjective. Hence there exists a basis of such that for any , and for any . For , let be the section defined as

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