** 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.

In the 2003 book Possessed: The Rise and Fall of Prince, author Alex Hahn says that Dickerson was reluctant to sign a three year contract and wanted to pursue other musical ventures.

Jessica Hahn says that that type of degradation had her authorization and " I am free to degrade myself only how I see fit!

* 1939 Otto Hahn and Fritz Strassmann bombard uranium salts with thermal neutrons and discover barium among the reaction products

Having won sprint events at the 1903 American and Canadian championships, Hahn — born in Dodgeville, Wisconsin, but running for the University of Michigan — was among the favourites at the 1904 Olympic Games in St. Louis, which was poorly attended by European athletes.

Kurt Hahn set up the field hockey team personally with Prince Philip humorously recounting a game against Elgin Academy's Ladies team and saying that he "... hoped that soon we shall be among the best Scottish girls ' teams.

The Philip Y. Hahn School of Nursing and Health Science is among the top 10 percent of graduate-level nursing programs according to the U. S. News & World Report (# 47 ).

In intergroup comparisons, high attitude similarity would lead to homogeneity among in-group members whereas low attitude similarity would lead to diversity among in-group members, promoting social attraction and achieving high group performance in different tasks ( Hahn & Hwang, 1999 ).

Hahn founded and is currently the President of the St. Paul Center for Biblical Theology, a Christian research center and think tank committed to the promotion of biblical literacy among the Catholic laity and biblical fluency among Catholic clergy.

Contraband camps had already been a fixture from early on in the war, and missionaries were already hard at work living among the contrabands, a point which was not lost on Steven Hahn who noted that:

Trailed in Belgrade in December 1946 with other SS and Gestapo officials and sentenced to death by hanging together with August Meissner, Wilhelm Fuchs, Josef Hahn, Ludwig Teichmann, Josef Eckert, Ernst Weimann, Richard Kaserer and Friedrich Polte.

Hahn is served by a number of ( mostly ) private bus operators that run regular services to Frankfurt am Main ( 1 h 45 min, via Frankfurt International Airport, Terminal 2 ), Cologne ( 2 h 15 min ), Luxembourg ( 1 h 45 min ) and a number of other cities in western Germany and the region.

" Meketibolodon ( Hahn 1993 ) is distinguished from the other genera Paulchoffatiidae by two characters: the tooth row is significantly convexly curved upwards, and the corpus mandibulae has angled margins ventrally ( Hahn and Hahn 1998b ).

In the beginning Hahn blended a traditional private school ethos, modelled on Eton and his experiences at Oxford, with a philosophy inspired by Plato ’ s The Republic and other aspects of ancient Greek history.

: Hahn believed that “ The Platonic view of education is that a nation must do all it can to make the individual citizen discover his own power and further more that the individual becomes a cripple in his or her point of view if he is not qualified by education to serve the community .” The idea of service at the school is thought to encourage students to gain a feeling of responsibility to aid other people and is implemented in creating an array of services that every student becomes apart of ( see below ).

In the beginning Hahn expressed his view that at many schools ball games had been given precedence over other activities and so, to start with, more focus was placed on seamanship and practical work than the playing of games.

This lemma is equivalent to the well-ordering theorem and the axiom of choice and implies major results in other mathematical areas like the Hahn – Banach theorem and Tychonoff's theorem, the existence of a Hamel basis for every vector space, and the existence of an algebraic closure for every field.

Prior to his term as mayor, Hahn served in several other capacities for the city of Los Angeles, including Deputy City Attorney ( 1975 – 1979 ), City Controller ( 1981 – 1985 ) and City Attorney ( 1985 – 2001 ).

Dewey's work influenced dozens of other prominent experiential models and advocates in the later 20th century, including Foxfire, service learning, Kurt Hahn and Outward Bound, and Paulo Freire.

Among other things, Bertie suggested to Hahn to write to Sir Henry Hallett Dale, who had been the president of the Royal Society, which he did.

However, Mayor Hahn actually was considering the appointment before other interests persuaded him in appointing William J. Bratton, a former police commissioner of Boston and New York City, to head the department.

Hahn is an Eagle Scout who received a merit badge in Atomic Energy and spent years tinkering with basement chemistry which sometimes resulted in small explosions and other mishaps.

In 1999, Hahn said that she played Bach more than any other composer and that she had played solo Bach pieces every day since she was eight.

, Hahn has given over 800 talks in the US and other countries on theological and biblical topics related to the Catholic faith and appears regularly on the Eternal Word Television Network ( EWTN ).

Air Armenia with a scheduled service to Frankfurt Hahn Airport, which was used as a hub for cargo from / to other points worldwide.

* Asking for Trouble ( 2005 ) by Jason Hahn, an 8-days journalist, who based his humour book on his experiences with living with two high-maintenance women, with free advice from his 2 male friends, one gay, the other married.

At Hahn AB, other wing personnel participated in a NATO exercise.

A music video for " Bebot " was filmed in and around Los Angeles in early July 2006, including in Kenneth Hahn Park, where Dr. Dre's " Nuthin ' but a " G " Thang " video was also filmed ; the video features primarily Filipinos, Filipino Americans and other Asian-Americans from the Los Angeles area.