Distributive "tetration", is this possible

[tommy1729]

I think if we want to disprove its existence we'd best look at this relation:
\( (^t a)\,\otimes_\mu\, b = \,^t(a\, \otimes_\mu\,b) \)

this seems like the most unlikely property for any operator to have.

yes , try a = sqrt(2) and t = oo

regards

tommy1729

-- unless you use my distributive formula --