TY  - JOUR
ID  - Gil2013
LB  - Gil2013
AU  - Gil', Michael
TI  - Inequalities for regularized determinants of operators with the Nakano type modulars
ST  - Inequalities for regularized determinants of operators with the Nakano type modulars
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 2
SP  - 283
EP  - 291
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.2.283
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.2.283
AB  - Let \(\{p_k\}\) be a nondecreasing sequence of integers, and \(A\) be a compact operator in a Hilbert space whose eigenvalues and singular values are \(\lambda_k(A)\) and \(s_k(A)\) \((k=1, 2, .... )\), respectively. We establish upper and lower bounds for the regularized determinant \[\prod_{k=1}^\infty (1-\lambda_k(A)){\rm exp}\;[\sum_{m=1}^{p_k-1} \frac{\lambda_k^m(A)}{m}],\mbox{ assuming that } \sum_{j=1}^{\infty} \frac{s_j^{p_j}(A/c)}{p_j}\lt \infty\] for a constant \(c\in (0,1)\).
KW  - Hilbert space
KW  - compact operators
KW  - regularized determinant
KW  - Nakano type modular
SN  - 1232-9274
ER  -