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We present a new and interesting extension theorem for concave operators as follows. Let X be a real linear space, and let (Y,K) be a real order complete PL space. Let the set A&#x2282;X&#x00D7;Y be convex. Let X0 be a real linear proper subspace of X, with &#x03B8;&#x2208;(AX&#x2212;X0)ri, where AX={x&#x02223;(x,y)&#x2208;A for some y&#x2208;Y}. Let g0:X0&#x2192;Y be a concave operator such that g0(x)&#x2264;z whenever (x,z)&#x2208;A and x&#x2208;X0. Then there exists a concave operator g:X&#x2192;Y such that (i) g is an extension of g0, that is, g(x)=g0(x) for all x&#x2208;X0, and (ii) g(x)&#x2264;z whenever (x,z)&#x2208;A

A New Extension Theorem for Concave Operators