A new class of operator ideals and approximation numbers

Abstract

In this study, we introduce the class of generalized Stolz mappings by generalized approximation numbers . Also we prove that the class of ℓ α p −type mappings are included in the class of generalized Stolz mappings by generalized approximation numbers and we define a new quasinorm equivalent with T α φ (p) . Further we give a new class of operator ideals by using generalized approximation numbers and symmetric norming function and we show that this class is an operator ideal.

Eigenvalues of s-type operators on $C(p)$ equipped with a pre-quasi norm

“…The multiplication operators and operator ideals theorems give an importance in functional analysis, since it has numerous applications in fixed point theorem, geometry of Banach spaces, spectral theory and eigenvalue distributions theorem etc. For more details see [3][4][5][6][7][8][9][10][11][12][13][14]). On sequence spaces, Mursaleen and Noman (see [15]) investigated the compact operators on some difference sequence spaces, Komal and Gupta (see [16]) studied the multiplication operators on Orlicz spaces equipped with the Luxemburg norm and Komal et al (see [17]) examined the multiplication operators on Cesáro sequence spaces equipped with the Luxemburg norm.…”

Eigenvalues of s-Type Operators on Prequasi Normed Ct,p

“…Summability, multiplication, and ideal operator theorems are very important in mathematical models and have numerous implementations, such as normal series theory, ideal transformations, geometry of Banach spaces, approximation theory, and fixed point theory. For more details, see [1][2][3][4][5][6][7][8][9][10][11]. By ℂ ℕ , ℓ ∞ , ℓ r , and c 0 , we denote the spaces of every, bounded, r-absolutely summable, and convergent to zero sequences of complex numbers.…”