## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 970

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in Li ( R ) L2 ( R ) and f is the

If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in Li ( R ) L2 ( R ) and f is the

**limit**in the norm of L2 ( R ) of the generalized sequence { Zef } . Hence , by Theorem 9 , of is the ...Page 1124

If En . E are in F and q ( En ) increases to the

If En . E are in F and q ( En ) increases to the

**limit**9 ( E ) , then it follows from what we have already proved that E , is an increasing sequence of projections and En S E. If Ec is the strong**limit**of En , then E SE and q ( E ) = 4 ...Page 1699

E E - E + + by Lemma 3.22 , Ψε Ê is the

E E - E + + by Lemma 3.22 , Ψε Ê is the

**limit**in the norm of H ( P ) ( L ) of a sequence { g ; } of functions in CO ( L ) . Putting ĝ ; ( x ) = 0 for x in C - L , it follows from Definition 3.15 that peFe is the**limit**in the norm of H ...### What people are saying - Write a review

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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero