In this paper we present how to apply a Berberian’s technique asymmetric Putnam–Fuglede theorems. particular, proved that if $$A,B\in \mathcal {B}(\mathcal {H})$$ belong the union of classes $$*$$ -paranormal operators, p-hyponormal dominant operators and class $$\mathcal {Y}$$ $$AX=XB^*$$ for some $$X\in , then $$A^{*}X=XB$$ . Moreover, gave new counterexample an theorem paranormal operators.

ABSTRACT It is currently fashionable to take Putnamian model-theoretic worries seriously for mathematics, but not discussions of ordinary physical objects and the sciences. However, I will argue that (under certain mild assumptions) merely securing determinate reference possibility suffices rule out kind nonstandard interpretations our number talk Putnam invokes. So, anyone who accepts should r...

If instead the tangents to C1 at P1, P2 are not perpendicular to L, then we claim there cannot be any point where C1 and C2 are tangent. Indeed, if we count intersections of C1 and C2 (by using C1 to substitute for y in C2, then solving for y), we get at most four solutions counting multiplicity. Two of these are P1 and P2, and any point of tangency counts for two more. However, off of L, any p...