16295

16295

لگاريتم عملگرهاي نرمال

كارشناسي ارشد

رياضي محض - آناليز رياضي

تيرماه 1395

دكتر محمدباقر قائمي

رياضي

1395/10/27

1/1/1900 12:00:00 AM

Abstract: Let A, B be normal bounded operators on a Hilbert space such that eA = eB . If the spectra of A an​d B are contained in a strip of the complex plane defined by jIm(z)j , we show that jAj = jBj. If B is only assumed to be bounded, then jAjB = BjAj . We give a formula for A 􀀀 B in terms of spectral projections of A an​d B are contained in a strip of the complex plane defined by R + i[(2k0 + 1); (2k1 + 1)]. Let X be a Banach space such that L(X) is the collection of all bounded linear operators on X. If T 2 L(X), Then the following conditions are equivalent: 1. T′ 2 L(X′) is a scalar-type operator of class X, 2. T 2 L(X) is strongly normal-equivalent, 3. there exist a compact subset Ω of C an​d a norm continuous representation : C(Ω) 7! X such that (z 7! z) = T; (z 7! 1) = I. And ifX be a Banach space which does not contain a subspace isomorphic to c0, Then T 2 L(X) is scalar-type spectral if an​d only if T satisfies any (and hence all) of the above conditions. Keywords: Exponential map, Normal operator, Scalar-type spectral, Subspace isomorphic