Polymath problem: Difference of two filters

My open problem first published in this my blog post (about pair-wise equality of four different expressions for differences of two filters) may be considered to be the next polymath problem.

Well, I realize that this may problem may be not ideal for polymath, because to approach a solution of this problem not inventing my techniques again one may need to read this my article. But maybe one may solve this problem without prior reading of my writings. I just don’t know what is the complexity behind my problem and whether is has an elementary solution. Nevertheless I would recommend to read my article before attacking the problem.

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