Browsing by Author "Durna, Nuh"

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    On the spectrum of the upper triangular double band matrix U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c
    (Ankara Üniversitesi, 2022) Durna, Nuh; Other; Other
    The upper triangular double band matrix U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) is defined on a Banach sequence space by U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) ( x n ) = ( a n x n + b n x n + 1 ) ∞ n = 0 where a x = a y , b x = b y for x ≡ y ( m o d 3 ) . The class of the operator U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) includes, in particular, the operator U ( r , s ) when a k = r and b k = s for all k ∈ N , with r , s ∈ R and s ≠ 0 . Also, it includes the upper difference operator; a k = 1 and b k = − 1 for all k ∈ N . In this paper, we completely determine the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c .