@Article{Gil2013,
author = "Gil', Michael",
title = "Inequalities for regularized determinants of operators with the Nakano type modulars",
journal = "Opuscula Math.",
year = "2013",
volume = "33",
number = "2",
pages = "283--291",
doi = "http://dx.doi.org/10.7494/OpMath.2013.33.2.283",
url = "http://dx.doi.org/10.7494/OpMath.2013.33.2.283",
abstract = "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 \(c\in (0,1)\).",
keywords = "Hilbert space, compact operators, regularized determinant, Nakano type modular",
issn = "1232-9274"
}