Notation Index
A (unitization of a C-algebra), 28
A, B, C and D (C-algebras), 2
A® B (minimal tensor product), 73
A ®max B (maximal tensor product), 73
A ><1"',r r (reduced crossed product), 118
A ><I"' r (full crossed product), 117
A* (double dual of a C-algebra), 5
A^0 P (opposite C-algebra), 211
A+ (positive elements in a C-algebra), 2
A1 (closed unit ball in a C-algebra), 2
A'P (multiplicative domain), 12
Asa (self-adjoints in a C-algebra), 2
JIB(H) (bounded (adjointable) linear
operators), 1, 137
C(G) (full groupoid C-algebra), 204
C(r) (full group C-algebra), 43
0(6) (graph C-algebra), 135
C~(G) (reduced groupoid C-algebra),
204
C~(r) (reduced group C-algebra), 42
c; (r) (right reduced group C-algebra),
42
C~(r) (uniform Roe algebra), 168
Cc(r, A) (finitely supported functions on
r with values in A), 116
qr] (complex group ring), 42
CA (cone over a C-algebra A), 251, 270
CP(E, B) (space of completely positive
maps), 9
c(7r) (central cover), 6
6.9r cg-boundary of r), 411
E9n An (co-direct sum), 107
E and F (operator systems or spaces), 2
{ei,j} (matrix units), 2
*(Hi, gi) (free product Hilbert module),
154
* v(Ai, Ei) (reduced amalgamated free
product), 155
:F(H) (full Fock space), 141
lFr (free group of rank r), 50
g ~(Am, \On,m) (generalized inductive
limit), 314
1t, /(, and .C (Hilbert spaces), 1
1t ® K (Hilbert spaces tensor product), 67
1t ®A/(, (interior tensor product of
Hilbert modules), 138
I <1A (ideal in a C*-algebra), 2
K(H) (compact operators), 1, 137
L^2 (A, E) (GNS Hilbert module), 138
L^2 (A,\O) (GNS Hilbert space), 2
L(r) (group von Neumann algebra), 43·
£^2 (separable, infinite-dimensional
Hilbert space), 1
e; ( n-dimensional Hilbert space), 1
£^00 (r) (complex bounded functions on r)'
42
.A (left regular representation), 42, 204
Mn(C) (n x n matrices), 1
M and N (von Neumann algebras), 2
M. (predual of a von Neumann algebra),
4
m'P (multiplier), 46
0(7-t) (Cuntz-Pimsner algebra), 143
Ilj Bj (£^00 -direct sum), 3
Prob(X) (regular Borel probability
measures), 48
Q(H) (Calkin algebra), 1
~ (real part of a complex number), 340
p (right regular representation), 42
S(A) (state space of a C*-algebra), 2
S1 (trace class operators), 1
S2 (Hilbert-Schmidt operators), 1- 503