## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 68

Page 1144

15 THEOREM. Let 1 < p < 00, and let the compact operator T in Hilbert space \)

have an anti-Hermitian part lying in the class C. Let y1,..., y, be non-overlapping,

differentiable arcs in the compler plane starting at the origin.

of ...

15 THEOREM. Let 1 < p < 00, and let the compact operator T in Hilbert space \)

have an anti-Hermitian part lying in the class C. Let y1,..., y, be non-overlapping,

differentiable arcs in the compler plane starting at the origin.

**Suppose**that eachof ...

Page 1393

(T). If t is a formal differential operator defined on the interval I, then the essential

spectrum of the closed operator Ti(t) in L2(I) is called the essential spectrum o.(1)

of r. 2 LEMMA. Let 3: be a Banach space, and

(T). If t is a formal differential operator defined on the interval I, then the essential

spectrum of the closed operator Ti(t) in L2(I) is called the essential spectrum o.(1)

of r. 2 LEMMA. Let 3: be a Banach space, and

**suppose**that 3 = }+9°, where J is ...Page 1602

(47) In [0, oo),

solutions f and g such that |f(s)ods = 0(e) and [.. g'(s)*ds = 0(e) Then the point %

belongs to the essential spectrum of t (Hartman and Wintner [14]). (48)

(47) In [0, oo),

**suppose**that the equation (2–1)f = 0 has two linearly independentsolutions f and g such that |f(s)ods = 0(e) and [.. g'(s)*ds = 0(e) Then the point %

belongs to the essential spectrum of t (Hartman and Wintner [14]). (48)

**Suppose**...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

4 Exercises | 879 |

Copyright | |

52 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

adjoint extension adjoint operator algebra analytic B-algebra B-space Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 Hence Hilbert space Hilbert-Schmidt operator identity inequality infinity integral interval kernel Lemma Let f Let Q linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real numbers satisfies sequence singular ſº solution spectral spectral theorem square-integrable subspace Suppose symmetric operator theory To(r To(t topology transform uniformly unique unitary vanishes vector zero