Abstract |
|
It is shown that if A and B are
operators on a separable complex Hilbert space and if
||| • ||| is any unitarily
invariant norm, then
| 2||||A|p +
|B|p
||| |
≤||||A +
B|p +
|A
− B|p
||| |
|
|
|
≤
2p−1||||A|p +
|B|p
||| |
|
|
for 2 ≤ p < ∞, and
| 2p−1||||A|p +
|B|p
||| |
≤||||A +
B|p +
|A
− B|p
||| |
|
|
|
≤
2||||A|p +
|B|p
||| |
|
|
for 0 < p ≤ 2. These inequalities are natural
generalizations of some of the classical Clarkson inequalities
for the Schatten p-norms.
Generalizations of these inequalities to larger classes of
functions including the power functions are also obtained.
|
Authors
|
Berkeley, California.