Properties of The Space of Bounded Linear Operators
- The space of all bounded linear operators from U to V is denoted by B(U,V) and is a normed vector space.
- If V is Banach, then so is B(U,V),
- from which it follows that dual spaces are Banach.
- For any A in B(U,V), the kernel of A is a closed linear subspace of U.
- If B(U,V) is Banach and U is nontrivial, then V is Banach.
Read more about this topic: Bounded Operator
Famous quotes containing the words properties of the, properties of, properties, space and/or bounded:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“It is the space inside that gives the drum its sound.”
—Hawaiian saying no. 1189, ‘lelo No’Eau, collected, translated, and annotated by Mary Kawena Pukui, Bishop Museum Press, Hawaii (1983)
“I could be bounded in a nutshell and count myself a king of
infinite space, were it not that I have bad dreams.”
—William Shakespeare (1564–1616)