On Kreǐn's extension theory of non-negative operators

The famous M.G. Kreın’s extension theory of nonnegative operators is being presented in elementary terms, building on the completion of nonnegative operator blocks. The present treatment includes the refinements to the theory due to T. Ando and K. Nishio. Moreover, the extension theory not only includes the case of operator extensions but also the case of relation (multivalued-operator) extensions.