** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals

* 1874 – Reynaldo Hahn, Venezuelan composer and conductor ( d. 1947 )

Banach spaces are named after the Polish mathematician Stefan Banach who introduced them in 1920 – 1922 along with Hans Hahn and Eduard Helly .< ref >

As a consequence of the Hahn – Banach theorem, this map is injective, and isometric.

* Hahn – Exton q-Bessel function

* Hahn – Banach theorem

In mathematics, the Hahn – Banach theorem is a central tool in functional analysis.

" Another version of Hahn – Banach theorem is known as Hahn – Banach separation theorem or the separating hyperplane theorem, and has numerous uses in convex geometry.

It is named for Hans Hahn and Stefan Banach who proved this theorem independently in the late 1920s, although a special case was proved earlier ( in 1912 ) by Eduard Helly, and a general extension theorem from which the Hahn – Banach theorem can be derived was proved in 1923 by Marcel Riesz.

The Hahn – Banach theorem states that if is a sublinear function, and is a linear functional on a linear subspace U ⊆ V which is dominated by on U,

Another version of Hahn – Banach theorem states that if V is a vector space over the scalar field K ( either the real numbers R or the complex numbers C ), if is a seminorm, and is a K-linear functional on a K-linear subspace U of V which is dominated by on U in absolute value,

This reveals the intimate connection between the Hahn – Banach theorem and convexity.

The Mizar project has completely formalized and automatically checked the proof of the Hahn – Banach theorem in the HAHNBAN file.

The theorem has several important consequences, some of which are also sometimes called " Hahn – Banach theorem ":

Another version of Hahn – Banach theorem is known as the Hahn – Banach separation theorem.

* 1926 – Carl Hahn, German businessman

* 1950 – James Hahn, American politician

* 1906 – Anna Marie Hahn, German-American serial killer ( d. 1938 )

A famous example of a theorem of this sort is the Hahn – Banach theorem.

Some of the notable mathematical concepts named after Banach include Banach spaces, Banach algebras, the Banach – Tarski paradox, the Hahn – Banach theorem, the Banach – Steinhaus theorem, the Banach-Mazur game, the Banach – Alaoglu theorem and the Banach fixed-point theorem.

It occurs in the proofs of several theorems of crucial importance, for instance the Hahn – Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that every nonzero ring has a maximal ideal and that every field has an algebraic closure.

This theory is due to Hans Hahn, who also showed that one obtains subfields when the number of ( non-zero ) terms is bounded by some fixed infinite cardinality.

* Huxie-Previously known as Need More, it is located somewhere between Hahn and Marble Hill.

He is also the author of the novels Die Festung ( 1995 ) ( The Fortress ), based on travels home across France in 1944, and Der Abschied ( 2000 ) ( The Parting ), about the nuclear-powered cargo vessel NS Otto Hahn.

Federally, Del Aire is located in California's 35th and 36th congressional districts, which have Cook PVIs of D + 33 and D + 11 respectively and is represented by Democrats Maxine Waters and Janice Hahn respectively.

Federally, Lennox is located in California's 36th congressional district, which has a Cook PVI of D + 11 and is represented by Democrat Janice Hahn.

The name meitnerium ( Mt ) was suggested in honor of the Austrian physicist Lise Meitner, a co-discoverer of protactinium ( with Otto Hahn ), and one of the discoverers of nuclear fission.

Charles Archibald " Archie " Hahn ( September 14, 1880 – January 21, 1955 ) was a German-American athlete, and one of the best sprinters in the early 20th century.

Judgment at Nuremberg provided key early roles for two actors who would later become prominent in TV and film during the 1960s: Werner Klemperer as Emil Hahn, one of the judges on trial, and William Shatner as Captain Byers.

Otto Hahn was one of only four nuclear-powered cargo vessels so far built.

Together with the Hahn – Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field.

Messner was the one who produced the money for the $ 265, 000 payment to Hahn, later billing PTL for work never completed on the Jerusalem Amphitheater at Heritage USA.

The film presents a fictionalized account of the post-World War II Nuremberg Trials, with Klemperer portraying Emil Hahn, a Nazi judge and one of the defendants at the trial.

While Mayor, Hahn created the Mayor's Office of International Trade and led two trade trips, one to Asia and one to Mexico.

Captain Horace Hahn, a member of the OSS, was one of the few Americans allowed to interrogate General Schellenberg.

According to a December 1944 Time article, Hahn " decided that she needed the steadying influence of a baby, but doubted if she could have one.

While there she received the news that Otto Hahn and Fritz Strassmann in Berlin had discovered that the collision of a neutron with a uranium nucleus produced the element barium as one of its byproducts.

In order to receive approval for construction from the Los Angeles County Board of Supervisors, Mrs. Chandler promised Kenneth Hahn that the building would be open free for the public for one day a year.

Later she appeared as one of the female singers on the debut album of the Echo Junkies, a duo formed in 2004 by Jon St. James and Skip Hahn.

Hahn began playing the violin one month before her fourth birthday in the Suzuki Program of Baltimore's Peabody Institute.

Jessica Corbin was one of these new additions, sharing hosting duties with Wil Wheaton and fellow TechTV veteran Hahn Choi.

part of the Moon, less than one crater diameter northwest of Hahn.

He is best known for being one of only three non-sherpa ( Dave Hahn and Ed Viesturs being the others ) to summit Mount Everest seven times, and has appropriately earned the moniker " Mr. Everest ".

Heineman defeated Democratic nominee David Hahn in the November 7, 2006, general election, capturing 73. 4 percent of the vote — one of the most lopsided victories for a gubernatorial race in Nebraska history.

In 1935, Boston's Jordan Marsh became one of the founders of New York City-based Allied Stores Corporation, a successor to Hahn Department Stores, Inc., a holding company founded in 1928.

Dick Miller, for example, has been in all of Dante's feature films and most of his television work, while Belinda Balaski, Archie Hahn, and Robert Picardo come in at close second, third, and fourth, with one less production each, respectively.

Both the annual highlight of the Friends ' activities and one of the cultural featurs of Cologne and the Rhineland, this purchase prize is dedicated to the memory of Wolfgang Hahn ( 1924-1987 ), chief conservator and painting restorer at Wallraf Richartz Museum / Museum Ludwig and one of Cologne's most far-sighted collectors.