Spectra of Lower Triangular Double-Band Infinite Matrices with Oscillatory Entries on ℓ1
Laloo Prasad Yadav
Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, Bihar, 846004, India.
Sanjay Kumar Mahto *
R.N.A.R. College, Samastipur (A Constituent Unit of L.N.M.U.), Darbhanga, Bihar, 848101, India.
*Author to whom correspondence should be addressed.
Abstract
This research investigates the spectral properties of a class of lower triangular double- band infinite matrices acting on the sequence space ℓ1. The matrix A is characterized by diagonal and sub-diagonal entries consisting of two oscillatory sequences, p and q possessing four and six distinct limit points, respectively. Through the application of functional analytic techniques and Goldberg’s subdivision, the spectrum, point spectrum, residual spectrum, and continuous spectrum are explicitly determined. The analysis demonstrates that while the point and continuous spectra are empty, the residual spectrum coincides with the entire spectrum, which is defined by a specific algebraic inequality involving the product of the oscillatory entries. These findings extend existing research in summability theory and provide a deeper understanding of the stability of linear operators in infinite-dimensional systems.
Keywords: Sequence space, infinite matrix, spectrum, point spectrum, residual spectrum, continuous spectrum