ABSTRACT
C~(X) (function space) 363 CT,tIJ (function space) 435 XD (characteristic function) 59 d(:c, y) (special metric) 140
~ (discriminant) 196 6(t, r) (delta type function) 220 6(8,0') (delta type function) 221 eA. (exponential operator) 25 e(t,s) (multiplier) 21 e(t, r, s) (multiplier) 3 ess c(a, b) (essential range) 102 essinf (essential infimum) 102 eSB sup (essential supremum) 38 Evo (function space) 244 l()x (fundamental function) 87 G(t, r) (Green function) 153 Go(t, r) (Green function) 155 7(s) (special function) 34 7(t, s) (special function) 46 71 (s) (special function) 73 700(s) (special function) 73 7(A) (measure of noncompactness) 7(M) (measure of noncompactness) 7n(M) (measure of noncompactness) H (Nemytskij operator) 11 H (t, r) (special integral operator)
108 108 142
22 224 224 224
22 28 37 43 41 274 41
ind (A) (index) 288 K (integral operator) 4 K(t) (integral operator) 2 IIKII. (special quasinorm) 117 ~(t, T) (characteristic function) 280 ~(3, 0') (characteristic function) 280 ~(A,~) (multiplicity) 291 L (partial integral operator) 4 L(8) (integral operator) 231 L,([a,b)) (Lebesgue space) 19 LM([a,b)) (Orlicz space) 86 L,(n, B) (Bochner space) 193 [L, ~ Lv} (function space) 8 [L, - Lv} (function space) 8 [LM ~ LN] (function space) 243 [LM - LN] (function space) 243 AOI (Lorentz space) 87 £(X, Y) (operator space) .cr (X, Y) (operator space) £p(X, Y) (operator space) .c;(X, Y) (operator space) .c(X) (operator algebra) £o(X) (operator algebra)
.c~(X) (operator algebra)
.cc(X) (operator algebra) £i(X) (operator algebra) .c,(X) (operator algebra) £m(X) (opera.tor algebra.)
£n(X) (operator algebra) 274 £p(X) (operator algebra) 251 £u,(X) (operator algebra) 43 £b(X) (operator algebra) 63 £HX) (operator algebra) 68 £i'-(X) (operator algebra) 69 £i'+(X) (operator algebra) 69 £i'o(X) (operator algebra) 69 £E(X) (operator algebra) 274 M (partial integral operator) 4 M(t) (integral operator) 231 M(u) (Young function) 242 ~ (D1easure) 214 ~ x v (product measure) 214 ~(Fj p) (growth function) 405 MOt (Marcinkiewicz space) 87 rot (operator algebra) 29 !Dln (operator algebra) 30 N (integral operator) 4 "+(A) (dimension) 291 ,,_(A) (dimension) 291 v (measure) 214 9ln (operator algebra) 177 w (Ljapunov exponent) 7 wo (Ljapunov exponent) 115 w· (Ljapunov-Bohl exponent) 7 Wo (Ljapunov-Bohl exponent) 7 n (measure space) 85
P (partial integral operator) 4 Pj (projection operator) 305 P+ (projection operator) 154 P_ (projection opera.tor) 154 PD (characteristic operator) 68 rC1(A) (spectral radius) 107 re.(A) (spectral radius) 323 rew(A) (spectral radius) 109 peA) (resolvent set) 287 Pre,(A) (regular resolvent set) 299 p(x, y) (special metric) 85 p(x, y) (special metric) 85 !)tc(X, Y) (multiplier class) 225 !)t,(X, Y) (kernel class) 225 9tm(X, Y) (kernel class) 225
~(X, Y) (kernel class) 225 1Yt,(X) (kernel class) 404 !5tm(X) (kernel class) 404 1Ytn(X) (kernel class) 404 Sc (contiuous part) 220 Sd (discrete part) 220 supp x (support) 89 supp N (support) 89 O'(A) (spectrum) 105 O',(A) (subspectrum) 287 O'd(A) (subspectrum) 287 O',(A) (subspectrum) 287 0'eb(A) (essential spectrum) 288
0'1111(A) (essential spectrum) 288 O'e.(A) (essential spectrum) 102 O'_(A) (essential spectrum) 102 O'+(A) (subspectrum) 288 O'_(A) (subspectrum) 288 sen, B) (Bochner space) 193 sen) (function space) 86 (T, AI (commutator) 123 U(p,q) (kernel class) 69 U(t, T) (evolution operator) 2 Uo(t, T) (evolution operator) 3 U(t) (evolution operator) 24 (U - VI (function space) 229 [U - VI (function space) 229 V(p, q) (kernel class) 70 YarD (variation) 262 W(a,,8) (kernel class) 71 wl(a,,8) (kernel class) 72 z* (rearrangement) 86 XO (regular part) 89 X' (associate space) 61 X* (dual space) 61 X, (function space) 404 X m (function space) 404 X" (function space) 404 X+ (function space) 180 X_ (function space) 180 X(w) (weighted space) 87
x+(w) (weighted space) 198 X_(w) (weighted space) 198 X Ea Y (decomposition) 303 X ® Y (tensor product) 290 :r ® y (tensor product) 290 Y/ X (multiplicator space) 224 31' (kernel class) 67 3; (kernel class) 69 3t (kernel class) 69
3~ (kernel class) 99 3(X) (kernel class) 69 3-(X) (kernel class) 100 3+(X) (kernel class) 100 3°(X) (kernel class) 100 3(X, Y) (kernel class) 234 2x (hyperspace) 385 (-, .) (duality pairing) 60 (-, .)+ (duality pairing) 151 (-, .)_ (duality pairing) 151 [-,.] (conic interval) 59 ]1 ·I[ (K-norm) 192
~ (special order) 242 -< (special order) 242
