Linear Operators: Spectral theory |
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Page 1092
... range , it is enough to prove the lemma in the special case that T has finite - dimensional domain and range . Note that if T has finite - dimensional range , T = n ET , where E is the orthogonal projection on the range of T. Thus T ...
... range , it is enough to prove the lemma in the special case that T has finite - dimensional domain and range . Note that if T has finite - dimensional range , T = n ET , where E is the orthogonal projection on the range of T. Thus T ...
Page 1134
... range of each projection E , in- variant , and the set F of projections E , λe C , subdiagonalizes T. To prove the second proposition of our theorem , we have only to verify that if E is any other orthogonal projection such that E≥ E ...
... range of each projection E , in- variant , and the set F of projections E , λe C , subdiagonalizes T. To prove the second proposition of our theorem , we have only to verify that if E is any other orthogonal projection such that E≥ E ...
Page 1137
... range , the following theorem states exactly such a result . 9 THEOREM . If 1 < p < ∞ , and if T is a compact quasi- nilpotent operator whose anti - Hermitian part belongs to the class C1 , then T itself belongs to the class C. We will ...
... range , the following theorem states exactly such a result . 9 THEOREM . If 1 < p < ∞ , and if T is a compact quasi- nilpotent operator whose anti - Hermitian part belongs to the class C1 , then T itself belongs to the class C. We will ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero