Airlines established in Greece must be majority owned and effectively controlled by EU states and/or nationals of EU states, unless otherwise provided for through an international agreement to which the EU is a signatory. In order to be recognised as Greek, aircraft must be (at a minimum) majority owned by EEA nationals or Greek legal entities majority owned by EEA nationals. In the case of limited liability companies, 75% of company shares must be owned by EEA nationals. Cabotage is reserved to national and EU airline companies. 
"Article 4 - Conditions for granting an operating licence:
An undertaking shall be granted an operating licence by the competent licensing authority of a Member State provided that:
[...]
(f) Member States and/or nationals of Member States own more than 50 % of the undertaking and effectively control it, whether directly or indirectly through one or more intermediate undertakings, except as provided for in an agreement with a third country to which the Community is a party; [...]" (Regulation (EC) No 1008/2008 on common rules for the operation of air services in the Community, Article 4(f))
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"Article 2 - Traffic conditions [...]
3 . The commercial transport of passengers and goods between two points of Greek territory as well as the transport of mail is reserved for Greek aircraft without prejudice to special and temporary and certainly not exclusive concessions to foreign aircraft, as long as they do not affect the interests of Greek air transport.
[...]
Article 18 - Aircraft nationality
 1. Greek aircraft are those aircraft, which belong to natural persons who have the citizenship of countries of the European Economic Area in a percentage greater than fifty percent (50%).
 2. Aircraft belonging to Greek legal entities by more than fifty percent (50%) are also recognized as Greek aircraft, provided that:
 a. in general partnerships, all partners are natural persons who are nationals of European Economic Area countries,
 b. in limited liability companies, all general partners are natural persons who are nationals of European Economic Area countries and the share capital is paid by two thirds of natural persons who are nationals of European Economic Area countries,
 c. in limited liability companies, the directors and three quarters of the partners are natural persons who are nationals of European Economic Area countries and three quarters of the company shares are owned by natural persons who are nationals of European Economic Area countries,
 d. in public limited companies all shares are registered and belong by an absolute majority to natural persons who are nationals of European Economic Area countries and two thirds of the members of the Board of Directors, its Chairman, the General Manager and any authorized or managing directors advisers are natural persons who are nationals of countries of the European Economic Area,
 e. in cooperatives or unions two thirds of the members, as well as all the members of the Board of Directors and the Supervisory Board are natural persons who have the citizenship of the countries of the European Economic Area.[...]" (Aviation Code (1815/1988), last amended by Law 3333/2005, Articles 2 and 18 [google translation based on unofficial text at kodiko.gr])
Regulation (EC) No 1008/2008 on common rules for the operation of air services in the Community, Article 4(f)
Aviation Code (1815/1988), last amended by Law 3333/2005, Articles 2 and 18 
[<a href="https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A02008R1008-20201218">Regulation</a>],[<a href="http://www.et.gr/idocs-nph/search/pdfViewerForm.html?args=5C7QrtC22wFWG2Ogb2ANFndtvSoClrL8cSHdHNezY5d5MXD0LzQTLWPU9yLzB8V68knBzLCmTXKaO6fpVZ6Lx3UnKl3nP8NxdnJ5r9cmWyJWelDvWS_18kAEhATUkJb0x1LIdQ163nV9K--td6SIufiWDmXHs3QQEjK2p4lAsYRV_7yMZcWloaY561F-Ujtm">Aviation Code (official)</a>],[<a href="https://www.kodiko.gr/nomothesia/document/260972">Aviation Code (unofficial)</a>]