Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 993
... follows from what has just been demonstrated that αy , = αvuv , ay , i.e. , ap is independent of V. Q.E.D. ато 1 ... follows from Lemma 3.6 that equation ( i ) holds for any open set with finite measure . It follows from the regularity ...
... follows from what has just been demonstrated that αy , = αvuv , ay , i.e. , ap is independent of V. Q.E.D. ато 1 ... follows from Lemma 3.6 that equation ( i ) holds for any open set with finite measure . It follows from the regularity ...
Page 996
... follows from the above equation that f * 90 . From Lemma 12 ( b ) it is seen that o ( f * q ) Co ( q ) and from Lemma 12 ( c ) and the equation tƒ = tf it follows that o ( f * q ) contains no interior point of o ( y ) . Hence o ( ƒ * q ) ...
... follows from the above equation that f * 90 . From Lemma 12 ( b ) it is seen that o ( f * q ) Co ( q ) and from Lemma 12 ( c ) and the equation tƒ = tf it follows that o ( f * q ) contains no interior point of o ( y ) . Hence o ( ƒ * q ) ...
Page 1124
... follows from what we have already proved that E , is an increasing sequence of projections and E , ≤ E. If E is the strong limit of E , then EE and ( E ) = q ( E ) . Thus , it follows as above that E = E. This proves that if q ( E ) is ...
... follows from what we have already proved that E , is an increasing sequence of projections and E , ≤ E. If E is the strong limit of E , then EE and ( E ) = q ( E ) . Thus , it follows as above that E = E. This proves that if q ( E ) is ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero