TY - JOUR
T1 - On the Decomposition of Hilbert Spaces
TT -
JF - IJMSI
JO - IJMSI
VL - 6
IS - 2
UR - http://ijmsi.ir/article-1-232-en.html
Y1 - 2011
SP - 1
EP - 7
KW - Numerical range
KW - Davis-Wielandt shell
KW - Spectra
KW - Conjugate of an operator.
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.
M3 10.7508/ijmsi.2011.02.001
ER -