If A#42;A#92;geAA#42; or, equivalently, #124;#92;#33;#124;Ah#124;#92;#33;#124;#92;ge#124;#92;#33;#124;A#42;h#124;#92;#33;#124; for all vectors h, then A is said to be a hyponormal operator. An operator A is said to be cohyponormal if A#42; is hyponormal.
Source: wiktionary