On a certain subclass of analytic functions defined by $q$-Sălăgean operator associated with operator on Hilbert space

Using a Hilbert space operator, we define a new subclass of analytic functions defined by $p$-valent $q$-Sălăgean operator and determine coefficient estimates, distortion bounds, radii of close-to-convexity, starlikeness, and convexity for the functions in this class. We also investigate extreme points and the modified Hadamard product.