چكيده به لاتين
Abstract:
Let A, B be normal bounded operators on a Hilbert space such that eA = eB . If the spectra of A and 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 and 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 and 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 and only if T satisfies any (and hence all) of the above conditions.
Keywords: Exponential map, Normal operator, Scalar-type spectral, Subspace isomorphic
