Index
AL-space, 87, 90
AM-compact operator, 313
AM-space, 87, 90
represented as Loo(7r), 152
with unit, 87
abstract integral operator, 154
additive semigroup of operators, 319
adjoint of resolvent, 190
adjoint of strictly singular operator, 142
adjoint operator, 66
algebra of operators, 304
non-transitive, 304, 305, 331
transitive, 306
unital, 304
algebraic complement of subspace, 136
algebraic homomorphism, 129
analytic function, 50, 205
annihilator, 19
of a set, 257
of a vector subspace, 19, 257
antisymmetry property, 20
approximate eigenvalue, 198, 222
approximate point spectrum, 198, 232
approximation of vectors in Eu, 104
approximation property, 122
Archimedean Riesz space, 22, 25, 72, 108,
212
ascent of operator, 68, 137, 210
atom, 72, 74, 352
in C(Q)-space, 352
atomic Banach lattice, 282
atomic measure space, 154
atomless Riesz space, 73
automatic continuity, 132
backward shift, 69, 286, 311
Banach function space, 154
Banach lattice, 332
atomic, 282
complex, 96
with mixed norm, 163
with order continuous norm, 71, 76, 90,
126, 329
Banach space
direct sum, 7, 195
quotient, 18
reflexive, 11, 40, 341, 367
renormed, 373
separable, 362
uniformly convex, 11, 338, 341, 342, 344
uniformly smooth, 338, 342-344
band, 24, 72, 75, 76, 106, 159, 265, 291
generated by a set, 24
generated by a vector, 24
generated by an ideal, 24
principal, 110
projection, 29, 321
band irreducibility, 290
band irreducible operator, 273, 276, 281
quasinilpotent, 292
band projection, 108
Bartle-Dunford-Schwartz theorem, 363
basic sequence, 39
basis, 31, 329
in C[0,1], 37
inL
p
[0,l] , 34
in a B-space, 31, 33
orthogonal, 244
orthonornal, 244
unconditional, 36, 40, 329
biorthogonal sequence, 40
379
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