There are no prerequisites.

# Riesz spaces in mathematical economics

The Arrow-Debreu model for exchange economies with a finite number of commodities and consumers.Kakutani fixed-point theorem.

A Walras equilibrium in a neoclassical exchange economy.Welfare theorems.

Riesz spaces. Linear functionals and linear operators.Riesz spaces of commodities and prices.Model for exchange economy with infinitedimensional space of commodities and countably many consumers.

C. D. Aliprantis, D. J. Brown, O. Burkinshaw: Existence and optimality of competitive equilibria, Springer-Verlag, Berlin, 1990.

C. D. Aliprantis: Problems in equilibrium theory, Springer-Verlag, Berlin, 1996.

C. D. Aliprantis, O. Burkinshaw: Locally solid Riesz spaces with applications to economics, Mathematical Surveys and Monographs 105, American Mathematical Society, Providence, RI, 2003.

Students learn about the application of the theory of Riesz spaces in mathematical economics. They get acquainted with

some models of exchange economies.

Knowledge and understanding:

Knowledge and understanding of the basic concepts of the theory Riesz spaces. The ability of its use in mathematical economics.

Application:

Using the theory of Riesz spaces on models of exchange economies.

Reflection:

Understanding of the theory and the ability to apply it to concrete examples.

Transferable skills:

Identifying and solving problems.Formulation of nonmathematical problems in mathematical language.Ability to use domestic and foreign literature.

Lectures, exercises, homeworks, consultations, seminars

Homeworks

Exam

grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Roman Drnovšek:

DRNOVŠEK, Roman. Triangularizing semigroups of positive operators on an atomic normed Riesz space. Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2000, let. 43, št. 1, str. 43-55. [COBISS-SI-ID 9480281]

DRNOVŠEK, Roman. On positive unipotent operators on Banach lattices. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2007, vol. 135, no. 12, str. 3833-3836. [COBISS-SI-ID 14382937]

DRNOVŠEK, Roman. An infinite-dimensional generalization of Zenger's lemma. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2012, vol. 388, iss. 2, str. 1233-1238. [COBISS-SI-ID 16214617]

Marko Kandić:

KANDIĆ, Marko. Sets of matrices with singleton spectra generated by positive matrices. Linear Algebra and its Applications. [Print ed.]. 2016, vol. 496, str. 463-474. ISSN 0024-3795. [COBISS-SI-ID 17602137]

DRNOVŠEK, Roman, KANDIĆ, Marko. Positive operators as commutators of positive operators. Studia Mathematica. 2019, tom 245, str. 185-200. ISSN 0039-3223. [COBISS-SI-ID 18407769]

KANDIĆ, Marko, VAVPETIČ, Aleš. The countable sup property for lattices of continuous functions. Journal of mathematical analysis and applications. [Print ed.]. Sep. 2018, vol. 465, iss. 1, str. 588-603. ISSN 0022-247X. [COBISS-SI-ID 18406489]