Self-adjoint square roots of positive self-adjoint bounded linear operators
نویسندگان
چکیده
منابع مشابه
Spectral Theorem for Bounded Self-adjoint Operators
Diagonalization is one of the most important topics one learns in an elementary linear algebra course. Unfortunately, it only works on finite dimensional vector spaces, where linear operators can be represented by finite matrices. Later, one encounters infinite dimensional vector spaces (spaces of sequences, for example), where linear operators can be thought of as ”infinite matrices”. Extendin...
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1 Definition of the Adjoint Let V be a complex vector space with an inner product < , and norm , and suppose that L : V → V is linear. If there is a function L * : V → V for which Lx, y = x, L * y (1.1) holds for every pair of vectors x, y in V , then L * is said to be the adjoint of L. Some of the properties of L * are listed below. Proof. Introduce an orthonomal basis B for V. Then find the m...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1972
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s001309150002616x