On the Decomposition of Hilbert Spaces
Hamidreza Afshin, Mostafa Ranjbar · 2011
Abstract. A basic relation between numerical range and Davis-Wielandt shell of an operator A acting on a Hilbert space with orthonormal basis ξ = {ei|i ∈ I} and its conjugate A ̄ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of A and Ā. A necessary and sufficient condition for A to be self-conjugate (A = Ā) is given using a subgroup of H.