Re: [harmonic] Singular values?
The same inequality holds good in a normed linear space, in the case of approximation numbers also.
It simply depends on the fact that the sum of two finite rank operators, one of rank less than or equal to k-1 and other less than or equal to n-1, will have rank less than or equal to n+k-2.
You can refer a book called 'operator ideals' by Piestch, A.
--- On Wed, 19/1/11, Zohreh Rahbani <zrahbani@...> wrote:
From: Zohreh Rahbani <zrahbani@...>
Subject: [harmonic] Singular values?
Date: Wednesday, 19 January, 2011, 18:43Dear all,
I'm dealing with a problem and I would be very thankful if someone could help me.
The following inequality is well known for singular values of a compact operators in Hilbert spaces:
s_(n+k-1)(T+L) <= s_(n)(T)+ s_(k)(L)
Is there any similar inequality for operators in a Banach spaces?
Any comment is very wellcome.