Associated with a dual pair is an injective linear map from to given by
There is an analogous injective map from to .
In particular, if either of or is finite dimensional, these maps are isomorphisms.
Read more about this topic: Dual Pair
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Famous quotes containing the word comment:
“Making social comment is an artificial place for an artist to start from. If an artist is touched by some social condition, what the artist creates will reflect that, but you cant force it.”
—Bella Lewitzky (b. 1916)
“The best thing about Sassy Seats is that grandmothers cannot figure out how they work and are in constant fear of the childs falling. This often makes them forget to comment on other aspects of the childs development, like why he is not yet talking or is still wearing diapers. Some grandmothers will spend an entire meal peering beneath the table and saying, Is that thing steady? rather than, Have you had a doctor look at that left hand?”
—Anna Quindlen (20th century)
“If I use the media, even with tricks, to publicise a black youth being shot in the back in Teaneck, New Jersey ... then I should be praised for it, and its more of a comment on them than me that it would take tricks to make them cover the loss of life.”
—Al, Rev. Sharpton (b. 1954)