On Catalan ideal convergent sequence spaces via fuzzy norm

The introduction of notion of regular matrix to act as a summability method has proved to be an impeccable tool in analysing the convergence of the otherwise non-convergent sequences. One such intriguing matrix namely Catalan matrix operator was initiated and studied in the settings of sequence spaces by Kara and Kara [Matrix transformations and compact operators on Catalan sequence spaces, J. Math. Anal. Appl. 498(1) (2001)]. In addition to studying their convergence in the setting of usual norm, a generalized version of the norm called fuzzy norm was introduced. This article explores the ideal convergence of sequences via Catalan matrix operator and fuzzy norm. Novel corresponding sequence spaces have been constructed, several interesting properties of the spaces have been studied and parallels have been drawn with some pre-existing notions. The research further explores algebraic and toplogical properties of the spaces.