Linear Operators: Spectral theory |
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Page 935
... quasi - nilpotent . Putnam [ 3 ] demonstrated that if A and B both commute with AB BA . then AB - BA is a quasi - nilpotent , thereby almost settling the conjecture . Vidav [ 1 ] has given a different proof of Putnam's result valid in ...
... quasi - nilpotent . Putnam [ 3 ] demonstrated that if A and B both commute with AB BA . then AB - BA is a quasi - nilpotent , thereby almost settling the conjecture . Vidav [ 1 ] has given a different proof of Putnam's result valid in ...
Page 1134
... quasi - nilpotent . Let ( a , b ) be an interval of the complement of C , and x its characteristic function . Let K11 ( s , t ) = c for s , t in [ a , b ] . Then , if ƒ is the vector χ f = [ x , 0 , 0 , . . . ] , it follows from what ...
... quasi - nilpotent . Let ( a , b ) be an interval of the complement of C , and x its characteristic function . Let K11 ( s , t ) = c for s , t in [ a , b ] . Then , if ƒ is the vector χ f = [ x , 0 , 0 , . . . ] , it follows from what ...
Page 1135
... quasi - nilpotent Hilbert - Schmidt operators is quasi - nilpotent , it follows from Lemma 5 that we may assume without loss of generality that for some finite M , K1 ; ( s , t ) ≤ M and that for some finite d , K ,, ( s , t ) = 0 , if ...
... quasi - nilpotent Hilbert - Schmidt operators is quasi - nilpotent , it follows from Lemma 5 that we may assume without loss of generality that for some finite M , K1 ; ( s , t ) ≤ M and that for some finite d , K ,, ( s , t ) = 0 , if ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero