Bronze Leonardo–Lucas sequence spaces and their geometric properties

In this paper, the Bronze Leonardo–Lucas matrix, denoted by $$\Gamma =(\acute{\text {BC}}_{{\mathfrak {n}}{\mathfrak {k}}})_{{{\mathfrak {n}}},{{{\mathfrak {k}}}} \in {\mathbb {N}}_0}$$ Γ = ( BC ´ n k ) n , k ∈ N 0 is defined by $$\begin{aligned} \acute{\text {BC}}_{{\mathfrak {n}}{\mathfrak {k}}} = {\left\{ \begin{array}{ll} \dfrac{3\acute{\text {BC}}_{\mathfrak {k}}}{4\acute{\text { BC}}_{\mathfrak {n}}+\acute{\text { BC}}_{{\mathfrak {n}}-1}+3{\mathfrak {n}}-10} & 1 \le {\mathfrak {k}} \le {\mathfrak {n}}, \ 0, & {\mathfrak {k}} > {\mathfrak {n}}, \end{array}\right. } \end{aligned}$$ BC ´ n k = 3 BC ´ k 4 BC ´ n + BC ´ n - 1 + 3 n - 10 1 ≤ k ≤ n , 0 , k > n , and $$\{\acute{\text {BC}}_{\mathfrak {k}}\}$$ { BC ´ k } corresponds to terms of the Bronze Leonardo–Lucas sequence. The sequence $$\{\acute{\text {BC}}_{\mathfrak {k}}\}$$ { BC ´ k } is defined by $$\begin{aligned} \acute{\text {BC}}_{\mathfrak {k}} = 3\acute{\text {BC}}_{{\mathfrak {k}}-1} + \acute{\text {BC}}_{{\mathfrak {k}}-2}-3~\text { for}~{{{\mathfrak {k}}}} \le 2,~ \acute{\text {BC}}_{0}=3,\acute{\text {BC}}_{1}=4. \end{aligned}$$ 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 $$ \alpha $$ α -, $$ \beta $$ β -, and $$ \gamma $$ γ -duals. Additionally, we examine certain specific operator ideals between these spaces. Lastly, the geometric characteristics of these sequence spaces are investigated.