<s>
In	O
mathematics	O
,	O
Kadison	B-Algorithm
transitivity	I-Algorithm
theorem	I-Algorithm
is	O
a	O
result	O
in	O
the	O
theory	O
of	O
C*	B-Algorithm
-algebras	I-Algorithm
that	O
,	O
in	O
effect	O
,	O
asserts	O
the	O
equivalence	O
of	O
the	O
notions	O
of	O
topological	O
irreducibility	O
and	O
algebraic	O
irreducibility	O
of	O
representations	O
of	O
C*	B-Algorithm
-algebras	I-Algorithm
.	O
</s>
<s>
It	O
implies	O
that	O
,	O
for	O
irreducible	O
representations	O
of	O
C*	B-Algorithm
-algebras	I-Algorithm
,	O
the	O
only	O
non-zero	O
linear	O
invariant	O
subspace	O
is	O
the	O
whole	O
space	O
.	O
</s>
<s>
If	O
the	O
C*	B-Algorithm
-algebra	I-Algorithm
acts	O
topologically	O
irreducibly	O
on	O
the	O
Hilbert	O
space	O
is	O
a	O
set	O
of	O
vectors	O
and	O
is	O
a	O
linearly	O
independent	O
set	O
of	O
vectors	O
in	O
,	O
there	O
is	O
an	O
in	O
such	O
that	O
.	O
</s>
<s>
If	O
the	O
C*	B-Algorithm
-algebra	I-Algorithm
acts	O
topologically	O
irreducibly	O
on	O
the	O
Hilbert	O
space	O
,	O
then	O
it	O
acts	O
algebraically	O
irreducibly	O
.	O
</s>
