mathematics

George Maltese

George Maltese is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand George Maltese rather than just read about it. In short: George John Maltese (June 24, 1931 in Middletown, Connecticut – October 23, 2009 in Middletown, Connecticut) was an American mathematician whose primary field of research was functional analysis. Life and career Maltese was born in Middletown, Connecticut, to a family of Italian ancestry.

Key takeaways

George Maltese belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect George Maltese to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of George Maltese from memory before moving on to harder problems.

Reference excerpt

George John Maltese (June 24, 1931 in Middletown, Connecticut – October 23, 2009 in Middletown, Connecticut) was an American mathematician whose primary field of research was functional analysis.

Life and career Maltese was born in Middletown, Connecticut, to a family of Italian ancestry. Between 1949 and 1953 he studied at the Wesleyan University. There he obtained his first degree, a (Bachelor of Arts, B.A.) in mathematics. From 1953 to 1954 he continued his studies as a Fulbright Fellow at the Goethe-University Frankfurt (Germany). From 1956 to 1960 he studied at Yale University (New Haven, Connecticut). There he earned his PhD with the dissertation Generalized Convolution Algebras and Spectral Representations supervised by Cassius Ionescu-Tulcea. During 1960–61 he worked as a NATO Fellow at the Georg-August-University of Göttingen (Germany). After lecturing as an instructor at the MIT in Cambridge, Massachusetts he joined in 1963 the University of Maryland, College Park, (Maryland). There he worked, interrupted by guest professorships at the University of Frankfurt (in 1966–67 and 1970–71), until 1973, from 1969 on as a Full Professor. In 1973 Maltese moved to Germany where he accepted a position as a Full Professor for mathematics at the University of Münster; there he worked until he retired in 1996. His research within the field of Functional analysis was concerned mainly with Harmonic analysis, the theory of Banach-algebras, integral representations in convex sets, and Korovkin theory. Maltese served as a guest professor at several universities, including the University of Palermo in 1970–71, the University of Bari in 1979, the University of Kuwait in 1977, the University of Bahrain in 1988–89, and the University of Oman in 1990–91. The Mathematics Genealogy Project lists 17 PhD students of Maltese, among others Ferdinand Beckhoff (Habilitation in 1994) and Anand Srivastav (Professor of Computer Science at the Christian-Albrechts-University of Kiel). Since 1987 he was a member of the Academia nazionale di szienze, lettere e arti di Palermo. Following his retirement Maltese went, together with his wife Marlene (née Kunz) back to Middletown and the Wesleyan University.

Selected papers Convex ideals and positive multiplicative forms in partially ordered algebras. Math. Scand. 9, 372–382 (1961). Spectral representations for solutions of certain abstract functional equations. Compos. Math. 15, 1–22 (1961). Spectral representations for some unbounded normal operators. Trans. Am. Math. Soc. 110, 79–87 (1964). mit R.S. Bucy: Extreme positive definite functions and Choquet’s representation theorem. J. Math. Anal. Appl. 12, 371–377 (1965). mit R.S. Bucy: A representation theorem for positive functionals on involution algebras. Math. Ann. 162, 364–367 (1966). Multiplicative extensions of multiplicative functionals in Banach algebras. Arch. Math. 21, 502–505 (1970). On Bauer’s characterization of extreme points. Math. Ann. 184, 326–328 (1970). Extensions of pure states in normed spaces. Rend. Circ. Mat. Palermo, II. Ser. 25, 83–88 (1976). Convexity methods and the Choquet boundary in Banach algebras. Boll. Unione Mat. Ital., V. Ser., A 15, 131–136 (1978). Integral representation theorems via Banach algebras. Enseign. Math., II. Sér. 25, 273–284 (1979). A remark on the existence of nonannihilating vectors and functionals in normed spaces. Boll. Unione Mat. Ital., V. Ser., A 17, 128–130 (1980). Prime ideals are dense in maximal ideals of continuous functions. Rend. Circ. Mat. Palermo, II. Ser. 30, 50–52 (1981). Extreme points of intervals in C * -algebras. Arch. Math. 45, 354–358 (1985). A simple proof of the fundamental theorem of finite Markov chains. Am. Math. Mon. 93, 629–630 (1986). mit Gerd Niestegge: A linear Radon–Nikodým type theorem for C * -algebras with applications to measure theory. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 14, No.2, 345–354 mit Regina Wille-Fier: A characterization of homomorphisms in certain Banach involution algebras. Stud. Math. 89, No.2, 133–143 (1988). Extreme positive functionals and ideals of finite codimension in commutative Banach * -algebras. Atti Semin. Mat. Fis. Univ. Modena 39, No.2, 569–580 (1991). A representation theorem for positive functionals on involution algebras (revisited). Boll. Unione Mat. Ital., VII. Ser., A 8, No.3, 431–438 (1994). Some remarks on the Riesz representation theorem in Hilbert space. Boll. Unione Mat. Ital., VII. Ser., B 11, No.4, 903–907 (1997). The role of convexity in existence theorems for invariant and hyperinvariant subspaces in Hilbert spaces. Rend. Circ. Mat. Palermo, II. Ser. 49, No.2, 381–390 (2000).

References Pamela Kalte et al.: American Men and Women of Science, Thomson Gale 2004 George John Maltese at the Mathematics Genealogy Project Mitgliederverzeichnis der Deutschen Mathematiker-Vereinigung 2007 http://www.wn-trauer.de/Traueranzeige/George-Maltese-2009-10-23 http://wwwmath.uni-muenster.de/historie/Dekane.pdf Oberwolfach Photo Collection (http://owpdb.mfo.de/person_detail?id=2719)

Illustrations

George Maltese: George Maltese — George Maltese

Worked examples

Example 1 — a first encounter with George Maltese

Start with the simplest possible case. Write down what George Maltese claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to George Maltese before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about George Maltese ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of George Maltese

In research: George Maltese appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses George Maltese in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: George Maltese is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1931 births, 2009 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for George Maltese outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study George Maltese in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what George Maltese means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain George Maltese out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is George Maltese in simple terms?

George John Maltese (June 24, 1931 in Middletown, Connecticut – October 23, 2009 in Middletown, Connecticut) was an American mathematician whose primary field of research was functional analysis. Life and career Maltese was born in Middletown, Connecticut, to a family of Italian ancestry.

Why does George Maltese matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study George Maltese?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on George Maltese.