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multiplicative representation
matrix 21
for resolvent of
quasi-Hermitian operator 110,
¬nite dimensional
113
operators 24, 27
quasiunitary operator 119
π-triangular matrice 69
estimate for norm of powers
operator in Hilbert space 151-
¬nite nilpotent matrices 18, 37
160
Hilbert-Schmidt Volterra op-
multiplicity of eigenvalue
erator 92
of matrix 3
Neumann-Schatten Volterra op-
of operator
erator 93
in a Hilbert space 77
estimate for norm of resolvent of
Hilbert-Schmidt operator 83
Neumann-Schatten ideal 78
matrix 11
nilpotency index 102
Neumann-Schatten operator 88
nilpotent part of
operators with Hilbert-Schmidt
compact operator 82
power 86
¬nite matrix 8
quasi-Hermitian operator 106
noncompact operator 99
quasiunitary operator 118
normal matrix 2
Euclidean norm 1
normal operator 76
Frobenius norm of matrix 2
positive selfadjoint operator 76
Hausdor¬ distance between spec- P -triangular operator 98
tra 49, 129
Hilbert-Schmidt ideal 78 quasi-Hermitian operator 98
Hilbert-Schmidt operator 78 quasinilpotent operator 77
Hilbert-Schmidt norm 2, 78 quasinormal operator 98
256 Index


quasiunitary operator 116

resolution of identity 98
maximal (m.r.i.) 98

Schur™s basis 7, 81
singular numbers of compact oper-
ators 78
spectral variation 49, 129

relative nilpotent part 164
relative P -triangular operator 164
relative spectral variation 167
root vectors 77

Trace class 78
trace of
matrix 3
linear operator 78
triangular representation of
compact operator 82
matrix 7
quasi-Hermitian operator 104
quasiunitary operator 116
regular function of operator 115

unitary operator 76

Volterra operator 77

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