A question in linear algebra

Hi,

I have a question in linear algebra.

Known: Q = {q_ij} is an semi-infinite upper-triangular matrix with 0<
q_ij < 1 and each row sum is strictly less than 1; vector g = [g_1,
g_2,...]' > 0 and g_i -g_{i-1} > 0 for all i.

Question: is there any special property (or requirement) of g for
satisfying inequality
(I-Q)g >=0 ?

I just know, if q_ij = k_{j-i}, i.e.,
Q = | k_0 k_1 ...... |
| 0 k_0 k_1 ....|
| 0 0 k_0 ... |
| ... ... |
if g satisfies g_i-g_{i-1} non-increasing, (I-Q)g >=0 holds. But for
general Q as defined
in above, I don't know if there is anything we can say about g?

Thanks,
Cloud

.