Let
H
H
be a complex Hilbert space and let
B
(
H
)
B(H)
be the algebra of all bounded linear operators on
H
H
. For
c
=
(
c
1
,
…
,
c
k
)
c=(c_{1},\dots ,c_{k})
, where
c
1
≥
⋯
≥
c
k
>
0
c_{1}\ge \cdots \ge c_{k}>0
and
p
≥
1
p\ge 1
, define the
(
c
,
p
)
(c,p)
-norm of
A
∈
B
(
H
)
A\in B(H)
by
\[
‖
A
‖
c
,
p
=
(
∑
i
=
1
k
c
i
s
i
(
A
)
p
)
1
p
,
\|A\|_{c,p}=\left (\sum _{i=1}^{k} c_{i} s_{i}(A)^{p}\right )^{\frac {1}{p}} ,
\]
where
s
i
(
A
)
s_{i}(A)
denotes the
i
i
th
s
s
-numbers of
A
A
. In this paper we study some basic properties of this norm and give a characterization of the extreme points of its closed unit ball. Using these results, we obtain a description of the corresponding isometric isomorphisms on
B
(
H
)
B(H)
.