Optimal range theorems for operators with p-th power factorable adjoints
نویسندگان
چکیده
منابع مشابه
5: Inner Products, Adjoints, Spectral Theorems, Self-adjoint Operators
Lemma 1.2 (An Eigenvector Basis Diagonalizes T ). Let V be an n-dimensional vector space over a field F, and let T : V → V be a linear transformation. Suppose V has an ordered basis β := (v1, . . . , vn). Then vi is an eigenvector of T with eigenvalue λi ∈ F, for all i ∈ {1, . . . , n}, if and only if the matrix [T ]ββ is diagonal with [T ] β β = diag(λ1, . . . , λn). Lemma 1.3. Let V be a fini...
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Let V and W be real or complex finite dimensional vector spaces with inner products 〈·, ·〉V and 〈·, ·〉W , respectively. Let L : V → W be linear. If there is a transformation L∗ : W → V for which 〈Lv,w〉W = 〈v, Lw〉V (1) holds for every pair of vectors v ∈ V and w in W , then L∗ is said to be the adjoint of L. Some of the properties of L∗ are listed below. Proposition 1.1. Let L : V →W be linear. ...
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ژورنال
عنوان ژورنال: Banach Journal of Mathematical Analysis
سال: 2012
ISSN: 1735-8787
DOI: 10.15352/bjma/1337014665