Bronze Leonardo–Lucas sequence spaces and their geometric properties

In this paper, the Bronze Leonardo–Lucas matrix, denoted by Γ =(BC_nk)_n,k ∈ N₀ Γ = ( BC ´ n k ) n , k ∈ N 0 is defined by $${aligned} {BC}_{{n}{k}} = {\{ {array}{ll} {3{BC}ₖ}{4{ BC}ₙ+{ BC}_{{n}-1}+3{n}-10} & 1 ≤ {k} ≤ {n}, \\ 0, & {k} > {n}, {array}. } {aligned}$$ BC ´ n k = 3 BC ´ k 4 BC ´ n + BC ´ n - 1 + 3 n - 10 1 ≤ k ≤ n , 0 , k > n , and $$\{{BC}ₖ\}BC ´ k corresponds to terms of the Bronze Leonardo–Lucas sequence. The sequence\{{BC}ₖ\}BC ´ k is defined by{aligned} {BC}ₖ = 3{BC}_{{k}-1} + {BC}_{{k}-2}-3~ for~{{{k}}} ≤ 2,~ {BC}₀=3,{BC}₁=4. {aligned}$$ BC ´ k = 3 BC ´ k - 1 + BC ´ k - 2 - 3 for k ≤ 2 , BC ´ 0 = 3 , BC ´ 1 = 4 . Using the Bronze Leonardo–Lucas matrix as a starting point, we define new matrix-domain sequence spaces related to the Bronze Leonardo–Lucas numbers. We further establish key aspects explored include the properties and inclusion relationships of these spaces, the construction of a Schauder basis, and the identification of their α α -, β β -, and γ γ -duals. Additionally, we examine certain specific operator ideals between these spaces. Lastly, the geometric characteristics of these sequence spaces are investigated.