TY - JOUR JF - IJMSI JO - IJMSI VL - 6 IS - 2 PY - 2011 Y1 - 2011/11/01 TI - On the Decomposition of Hilbert Spaces TT - N2 - 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. SP - 1 EP - 7 AU - Afshin, H.R. AU - Ranjbar, M.A. AD - KW - Numerical range KW - Davis-Wielandt shell KW - Spectra KW - Conjugate of an operator. UR - http://ijmsi.ir/article-1-232-en.html DO - 10.7508/ijmsi.2011.02.001 ER -