TY - JOUR

T1 - Distribution of Eigenvalues of Nuclear Operators and Grothendieck-Lidskii Type Formulas

AU - Reinov, O.I.

AU - Latif, Q.

PY - 2013

Y1 - 2013

N2 - We study spectral properties of quasinormed operator ideals N r,p, r ∈ (0, 1], p ∈ [1, 2], and the corresponding approximation properties AP r,p. We prove that the ideal N r,p is of spectral type s, where 1/s = 1/r-1/p+1/2, and obtain new trace formulas similar to the classical Crothendieck-Lidskii formulas. We obtain a negative answer to the following question: for 0 <s <1 and T ∈ L(X,X) whether an operator T is s-nuclear if its adjoint T * is s-nuclear? Bibliography: 19 titles. © 2013 Springer Science+Business Media New York.

AB - We study spectral properties of quasinormed operator ideals N r,p, r ∈ (0, 1], p ∈ [1, 2], and the corresponding approximation properties AP r,p. We prove that the ideal N r,p is of spectral type s, where 1/s = 1/r-1/p+1/2, and obtain new trace formulas similar to the classical Crothendieck-Lidskii formulas. We obtain a negative answer to the following question: for 0 <s <1 and T ∈ L(X,X) whether an operator T is s-nuclear if its adjoint T * is s-nuclear? Bibliography: 19 titles. © 2013 Springer Science+Business Media New York.

U2 - 10.1007/s10958-013-1455-x

DO - 10.1007/s10958-013-1455-x

M3 - Article

SP - 312

EP - 329

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -