Volume 6, Issue 2 (11-2011)                   IJMSI 2011, 6(2): 1-7 | Back to browse issues page

DOI: 10.7508/ijmsi.2011.02.001

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Afshin H, Ranjbar M. On the Decomposition of Hilbert Spaces. IJMSI. 2011; 6 (2) :1-7
URL: http://ijmsi.ir/article-1-232-en.html


Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ 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 $bar{A}$. A necessary and sufficient condition for $A$ to be self-conjugate ($A=bar{A}$) is given using a subgroup of H.

Type of Study: Research | Subject: General

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