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, Berlin : Springer, cop. 1990.
- C. D. Aliprantis, O. Burkinshaw: Locally solid Riesz spaces with applications to economics, 2nd ed., Providence : American Mathematical Society, cop. 2003.
- C. D. Aliprantis: Problems in equilibrium theory, Berlin : Springer, 1996.

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]